https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:foundation-algebra/x2f8bb11595b61c86:algebra-overview-history/v/the-beauty-of-algebra 2023-11-15T19:12:44.061361401Z The beauty of algebra Algebra is a language that helps us understand the world around us. It's not just about numbers, it's about abstract ideas that can be applied to many areas like economics, physics, and even the fundamental structure of the universe. Sal Khan video https://cdn.kastatic.org/googleusercontent/I0LsE6ScprrzTB8r6smxaLV0ozwZmcmEJEZvjn1Rkqs37VcvA2JLjIlpz-oRRj04Yt-rxTsE_UEihni4H6DideGC The beauty of algebra Algebra is a language that helps us understand the world around us. It's not just about numbers, it's about abstract ideas that can be applied to many areas like economics, physics, and even the fundamental structure of the universe. https://cdn.kastatic.org/ka-youtube-converted/kpCJyQ2usJ4.mp4/kpCJyQ2usJ4.mp4 607 Algebraic expressions and operations with monomials, binomials, and multinomials https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:foundation-algebra/x2f8bb11595b61c86:algebra-overview-history/v/descartes-and-cartesian-coordinates 2022-11-16T04:22:43.7414897Z Intro to the coordinate plane Descartes created a system of two perpendicular axes (the x and y axes) which could be used to plot points in a plane. This enabled the visualization of algebraic equations in geometric form. For example, a linear equation like y = 2x + 1 could be plotted as a line on the coordinate plane, while a quadratic equation like y = x^2 could be plotted as a parabola. This linked algebra and geometry through the use of graphs. Sal Khan video https://cdn.kastatic.org/googleusercontent/b_wyHsydMfQR3qFOjpW-IBcpbheOeQU_SAGUN9VHIcsx48s4w9Qovu-tBH6i6BLEZhIDhfQEu-VpcvP91LLBh4vc Intro to the coordinate plane Descartes created a system of two perpendicular axes (the x and y axes) which could be used to plot points in a plane. This enabled the visualization of algebraic equations in geometric form. For example, a linear equation like y = 2x + 1 could be plotted as a line on the coordinate plane, while a quadratic equation like y = x^2 could be plotted as a parabola. This linked algebra and geometry through the use of graphs. https://cdn.kastatic.org/ka-youtube-converted/N4nrdf0yYfM.mp4/N4nrdf0yYfM.mp4 682 Algebraic expressions and operations with monomials, binomials, and multinomials https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:foundation-algebra/x2f8bb11595b61c86:algebra-overview-history/v/why-all-the-letters-in-algebra 2022-11-16T04:22:43.7414897Z Why all the letters in algebra? In algebra, we often want to work with general concepts instead of specific numbers. Using letters allows us to represent quantities that could change or that we don't know the value of yet. Letters can also be used to generalize formulas or equations. Sal Khan video https://cdn.kastatic.org/googleusercontent/DYzc1GKg7ulEt11yvpBUYCJCccI70fpUzFfKbjpVXgj0Tgolm08tPquneqdus8EZQcQZoQ2KOe8ex0wTHlcPoF8 Why all the letters in algebra? In algebra, we often want to work with general concepts instead of specific numbers. Using letters allows us to represent quantities that could change or that we don't know the value of yet. Letters can also be used to generalize formulas or equations. https://cdn.kastatic.org/ka-youtube-converted/Tm98lnrlbMA.mp4/Tm98lnrlbMA.mp4 184 Algebraic expressions and operations with monomials, binomials, and multinomials https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:foundation-algebra/x2f8bb11595b61c86:intro-variables/v/what-is-a-variable 2023-05-23T10:28:13.689545116Z What is a variable? Variables in math are symbols, often letters, that represent different values in various situations. They help us understand and solve problems with changing values. For example, when calculating total earnings at a job with an hourly wage plus tips, a variable can represent the fluctuating tips, making it easier to determine total income. Sal Khan video https://cdn.kastatic.org/googleusercontent/Z0Ew0H4CUDZ7Hc0NbhfLe904T2e_lMEyScP69jTH-2Kcauq4mxzwzwDS-yQlWeQlDKGfOS3-podwVZQRor01fOc What is a variable? Variables in math are symbols, often letters, that represent different values in various situations. They help us understand and solve problems with changing values. For example, when calculating total earnings at a job with an hourly wage plus tips, a variable can represent the fluctuating tips, making it easier to determine total income. https://cdn.kastatic.org/ka-youtube-converted/tHYis-DP0oU.mp4/tHYis-DP0oU.mp4 198 Algebraic expressions and operations with monomials, binomials, and multinomials https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:foundation-algebra/x2f8bb11595b61c86:intro-variables/v/why-aren-t-we-using-the-multiplication-sign 2023-05-23T10:28:13.689545116Z Why aren't we using the multiplication sign? In algebra, representing multiplication with variables can be tricky due to the similarity between the variable "x" and the multiplication symbol. To avoid confusion, use alternative methods like 2⋅x, 2(x), or 2x. Practice evaluating expressions by substituting given values for variables and following the order of operations. Sal Khan video https://cdn.kastatic.org/googleusercontent/ktQxtEIS88xXcToePo4nuRJMGsrWlUaS9br45MuAwXBTu7v9IBQei-LLD-qTcmsKKL7X8KJ8ahrPC9ne2cgsdNPk Why aren't we using the multiplication sign? In algebra, representing multiplication with variables can be tricky due to the similarity between the variable "x" and the multiplication symbol. To avoid confusion, use alternative methods like 2⋅x, 2(x), or 2x. Practice evaluating expressions by substituting given values for variables and following the order of operations. https://cdn.kastatic.org/ka-youtube-converted/vDaIKB19TvY.mp4/vDaIKB19TvY.mp4 298 Algebraic expressions and operations with monomials, binomials, and multinomials https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:poly-arithmetic/x2ec2f6f830c9fb89:poly-add-sub/v/adding-and-subtracting-polynomials-1 2023-08-11T17:38:48.446343948Z Adding polynomials Learn how to simplify polynomials by combining like terms! Discover the power of adding and subtracting terms with the same degree of x. Uncover the magic of removing parentheses and grouping similar terms together to simplify complex expressions. Master the art of polynomial simplification! Sal Khan video https://cdn.kastatic.org/googleusercontent/P52_7TkuPy7FOhq7-OePwtVYkcBA9-pAdD1w7Uvek40918VCfTIlt6TgXnQzEE4212lDDjIebIeAbdfvLzdkO0lq Adding polynomials Learn how to simplify polynomials by combining like terms! Discover the power of adding and subtracting terms with the same degree of x. Uncover the magic of removing parentheses and grouping similar terms together to simplify complex expressions. Master the art of polynomial simplification! https://cdn.kastatic.org/ka-youtube-converted/ahdKdxsTj8E.mp4/ahdKdxsTj8E.mp4 121 Algebraic expressions and operations with monomials, binomials, and multinomials https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:poly-arithmetic/x2ec2f6f830c9fb89:poly-add-sub/e/adding_and_subtracting_polynomials 2024-05-02T20:40:27.893470044Z Add polynomials (intro) Example: Add (2x²-3) and (7x³-4x+1). Tomer Gal exercise https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:poly-arithmetic/x2ec2f6f830c9fb89:poly-add-sub/v/subtracting-polynomials 2023-08-11T17:38:48.446343948Z Subtracting polynomials Master the art of adding and subtracting polynomials! Learn how to distribute negative signs across terms, combine like terms, and simplify expressions. This skill is key to understanding algebra and making math easier. Sal Khan video https://cdn.kastatic.org/googleusercontent/PGR9Z2IOnfKh7MWus7JU-aNIEKgaRIVq3fXAoZAK1UYQVq8sSroW476cJgoMTZFxYm-113UG20-1qy96K_DMxks Subtracting polynomials Master the art of adding and subtracting polynomials! Learn how to distribute negative signs across terms, combine like terms, and simplify expressions. This skill is key to understanding algebra and making math easier. https://cdn.kastatic.org/ka-youtube-converted/5ZdxnFspyP8.mp4/5ZdxnFspyP8.mp4 127 Algebraic expressions and operations with monomials, binomials, and multinomials https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:poly-arithmetic/x2ec2f6f830c9fb89:poly-add-sub/e/subtract-polynomials 2025-06-26T20:46:37.500606524Z Subtract polynomials (intro) Example: Evaluate (4x²-3) - (3x³-3x+2). Tomer Gal exercise https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:poly-arithmetic/x2ec2f6f830c9fb89:mono-by-poly/v/multiply-monomials-intro 2023-08-11T17:38:48.446343948Z Multiplying monomials Learn how to multiply monomials like a pro! Discover how to multiply numbers and variables separately, then combine them for the final answer. Explore how exponent properties come into play when multiplying variables. Dive into examples with different variables for variety. video https://cdn.kastatic.org/ka_thumbnails_cache/5bbc3cb7-ec07-4772-bb7d-ed56cfeaa9e1_1280_720_base.png Multiplying monomials Learn how to multiply monomials like a pro! Discover how to multiply numbers and variables separately, then combine them for the final answer. Explore how exponent properties come into play when multiplying variables. Dive into examples with different variables for variety. https://cdn.kastatic.org/ka-youtube-converted/7EplN4Ch98Q.mp4/7EplN4Ch98Q.mp4 196 Algebraic expressions and operations with monomials, binomials, and multinomials https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:poly-arithmetic/x2ec2f6f830c9fb89:mono-by-poly/e/finding-the-product-of-two-monomials 2025-01-22T07:22:50.02175738Z Multiply monomials Express the product of two monomial expressions as a single monomial Tomer Gal exercise https://www.khanacademy.org/math/algebra-home/alg-polynomials/alg-multiplying-monomials/v/multiplying-and-dividing-monomials-1 2020-12-28T16:56:57Z Multiplying monomials to find area: two variables Sal expresses the area of a rectangle with length 4xy and width 2y as a monomial. Sal Khan video https://cdn.kastatic.org/googleusercontent/L4I6X47Vv-02xy3zEHBU6keU_lO1MLzZdMWyyun7XbEC7Bz-rQzh7E3X5JjV4KFGEwTzn-bjA6XRXnRsMNfRVi8 Multiplying monomials to find area: two variables Sal expresses the area of a rectangle with length 4xy and width 2y as a monomial. https://cdn.kastatic.org/ka-youtube-converted/p_61XhXdlxI.mp4/p_61XhXdlxI.mp4 112 Algebraic expressions and operations with monomials, binomials, and multinomials https://www.khanacademy.org/math/algebra-home/alg-polynomials/alg-multiplying-monomials/v/multiplying-monomials 2020-12-28T16:56:56Z Multiplying monomials to find area Learn to express the area of a rectangle with length 4y and width 2y as a monomial. Sal Khan video https://cdn.kastatic.org/googleusercontent/e8oh7CddfBHVN3HznO7LObFEd2f5vBkI540UbQMoqpZ5vGo9MtNsd688RjoE0cYy66lwxrzicxxOzD5Q6BhU-AE Multiplying monomials to find area Learn to express the area of a rectangle with length 4y and width 2y as a monomial. https://cdn.kastatic.org/ka-youtube-converted/ssY1dFl7d30.mp4/ssY1dFl7d30.mp4 65 Algebraic expressions and operations with monomials, binomials, and multinomials https://www.khanacademy.org/math/algebra-home/alg-polynomials/alg-multiplying-monomials/v/missing-values-in-monomial-multiplication 2022-10-07T01:44:59.407126867Z Multiplying monomials challenge Sal finds the values of coefficients a and b that make (3x^a)(bx^4)=-24x^6 true for all x-values. video https://cdn.kastatic.org/ka_thumbnails_cache/c3a20d36-9b53-4593-8455-fbafa2baabd5_1280_720_base.png Multiplying monomials challenge Sal finds the values of coefficients a and b that make (3x^a)(bx^4)=-24x^6 true for all x-values. https://cdn.kastatic.org/ka-youtube-converted/mzULbezO6iA.mp4/mzULbezO6iA.mp4 212 Algebraic expressions and operations with monomials, binomials, and multinomials https://www.khanacademy.org/math/algebra-home/alg-polynomials/alg-multiplying-monomials/e/multiply-monomials-challenge 2026-01-21T14:10:46.416761336Z Multiply monomials (advanced) More challenging multiplying monomial problems like find the area or find missing values to make an equation true. Tomer Gal exercise https://www.khanacademy.org/math/algebra-home/alg-polynomials/alg-multiplying-monomials/a/multiplying-monomials-review 2024-10-13T23:08:26.856971738Z Multiplying monomials review A monomial is a polynomial with just one term. For example, 2a⁵ is a monomial. This article reviews how to multiply monomials (e.g., 2a⁵ · 3a² = 6a⁷ ). article https://www.khanacademy.org/math/algebra-home/alg-rational-expr-eq-func/alg-simplify-rational-expressions/v/dividing-monomials 2020-11-06T18:53:42Z Simplifying rational expressions (old video) Sal simplifies (28b^6)/(7b) as 4b^5. Sal Khan video https://cdn.kastatic.org/googleusercontent/YIX5hMtLFv-774qNYaASvOSy4NpDRsd33hhj30mbM4hj1OxIk2qIjy--02zhQi1ZWpOaVA4-UJtFpc1pIO8Sso4D Simplifying rational expressions (old video) Sal simplifies (28b^6)/(7b) as 4b^5. https://cdn.kastatic.org/ka-youtube-converted/4Eax48gDg9g.mp4/4Eax48gDg9g.mp4 56 Algebraic expressions and operations with monomials, binomials, and multinomials https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:poly-arithmetic/x2ec2f6f830c9fb89:mono-by-poly/v/area-model-of-monomial-polynomial-multiplication 2023-08-11T17:55:55.170540272Z Multiplying monomials by polynomials: area model Discover how to calculate the area of complex shapes using algebra! By breaking down a rectangle into smaller parts, we can find the total area by multiplying the height and width of each part. This method introduces us to the concept of multiplying monomials by polynomials. video https://cdn.kastatic.org/ka_thumbnails_cache/160a6172-8ab7-46fe-9f7a-cc52fa53efb7_1280_720_base.png Multiplying monomials by polynomials: area model Discover how to calculate the area of complex shapes using algebra! By breaking down a rectangle into smaller parts, we can find the total area by multiplying the height and width of each part. This method introduces us to the concept of multiplying monomials by polynomials. https://cdn.kastatic.org/ka-youtube-converted/bkZYILrmFRU.mp4/bkZYILrmFRU.mp4 94 Algebraic expressions and operations with monomials, binomials, and multinomials https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:poly-arithmetic/x2ec2f6f830c9fb89:mono-by-poly/e/multiply-monomials-by-polynomials-intuition 2021-07-29T22:44:48.94944018Z Multiply monomials by polynomials: area model Use area to understand how to multiply monomials by polynomials. Tomer Gal exercise https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:poly-arithmetic/x2ec2f6f830c9fb89:mono-by-poly/v/multiplying-monomials-by-polynomials 2023-08-11T17:55:55.170540272Z Multiplying monomials by polynomials Discover how to multiply monomials by polynomials using the distributive property. Learn to simplify expressions by multiplying coefficients and adding exponents. Get a handle on negative terms and see how they affect the final result. It's all about breaking down complex problems into simpler steps! Sal Khan video https://cdn.kastatic.org/googleusercontent/36lIyUQRFUt_s7RG9QyVMHhVvipyJ0bxeT77Fgf9KIkaSTjCkOrXGOad8iecfZoqJOPQh5MazVHHf9RIa66Rp3-8 Multiplying monomials by polynomials Discover how to multiply monomials by polynomials using the distributive property. Learn to simplify expressions by multiplying coefficients and adding exponents. Get a handle on negative terms and see how they affect the final result. It's all about breaking down complex problems into simpler steps! https://cdn.kastatic.org/ka-youtube-converted/pD2-H15ucNE.mp4/pD2-H15ucNE.mp4 163 Algebraic expressions and operations with monomials, binomials, and multinomials https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:poly-arithmetic/x2ec2f6f830c9fb89:mono-by-poly/e/finding-the-product-of-a-monomial-and-a-polynomial 2025-01-22T07:22:50.02175738Z Multiply monomials by polynomials Use the distributive property to express the product of a monomial and a polynomial as a single polynomial. Tomer Gal exercise https://www.khanacademy.org/math/algebra-home/alg-polynomials/alg-multiplying-polynomials-by-monomials/v/missing-values-in-monomial-polynomial-multiplication 2022-10-07T01:44:59.407126867Z Multiplying monomials by polynomials challenge Sal finds the values of coefficients c, d, and f that make -2y(y²+cy-3)=dy³+12y²+fy true for all y-values. video https://cdn.kastatic.org/ka_thumbnails_cache/1c61fd58-9f47-4010-8c33-0e2268394701_1280_720_base.png Multiplying monomials by polynomials challenge Sal finds the values of coefficients c, d, and f that make -2y(y²+cy-3)=dy³+12y²+fy true for all y-values. https://cdn.kastatic.org/ka-youtube-converted/NADPP4wlo1Q.mp4/NADPP4wlo1Q.mp4 258 Algebraic expressions and operations with monomials, binomials, and multinomials https://www.khanacademy.org/math/algebra-home/alg-polynomials/alg-multiplying-polynomials-by-monomials/e/multiply-monomials-by-polynomials-challenge 2026-01-21T14:10:46.416761336Z Multiply monomials by polynomials challenge Example: Find the values of the variables to make the following equation true -11(y²-cy+2) = dy²+33y-f. Tomer Gal exercise https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:poly-arithmetic/x2ec2f6f830c9fb89:mono-by-poly/a/multiplying-monomials-by-polynomials-review 2024-12-09T04:15:44.01032926Z Multiplying monomials by polynomials review We use the distributive property to multiply monomials by polynomials. For example, 2x(3x+7) = 6x^2+14x. This article provides a brief review of the topic and gives you a couple of practice problems to try on your own. article