https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratics-multiplying-factoring/x2f8bb11595b61c86:factor-perfect-squares/v/identifying-perfect-square-trinomials 2022-10-06T23:01:00.745424633Z Identifying perfect square form Sal shows how we can identify that a trinomial has the "perfect square" form. video https://cdn.kastatic.org/ka_thumbnails_cache/047b2592-ee51-42a7-99ce-80bf83c0ec6d_1280_720_base.png Identifying perfect square form Sal shows how we can identify that a trinomial has the "perfect square" form. https://cdn.kastatic.org/ka-youtube-converted/4STGvuoBi5U.mp4/4STGvuoBi5U.mp4 277 Factorization through algebraic identities https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratics-multiplying-factoring/x2f8bb11595b61c86:factor-perfect-squares/v/perfect-square-factorization-intro 2022-10-06T23:01:00.745424633Z Perfect square factorization intro When an expression has the general form a²+2ab+b², then we can factor it as (a+b)². For example, x²+10x+25 can be factored as (x+5)². This method is based on the pattern (a+b)²=a²+2ab+b², which can be verified by expanding the parentheses in (a+b)(a+b). video https://cdn.kastatic.org/ka_thumbnails_cache/65b779ae-9d58-4d2d-ab39-c5bde1a9f75b_1280_720_base.png Perfect square factorization intro When an expression has the general form a²+2ab+b², then we can factor it as (a+b)². For example, x²+10x+25 can be factored as (x+5)². This method is based on the pattern (a+b)²=a²+2ab+b², which can be verified by expanding the parentheses in (a+b)(a+b). https://cdn.kastatic.org/ka-youtube-converted/JX5Zvh6swmo.mp4/JX5Zvh6swmo.mp4 319 Factorization through algebraic identities https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratics-multiplying-factoring/x2f8bb11595b61c86:factor-perfect-squares/a/factoring-quadratics-perfect-squares 2023-07-28T22:30:23.739634445Z Factoring quadratics: Perfect squares Learn how to factor quadratics that have the "perfect square" form. For example, write x²+6x+9 as (x+3)². article https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratics-multiplying-factoring/x2f8bb11595b61c86:factor-perfect-squares/e/intro-to-factoring-perfect-squares 2025-01-15T08:58:52.349960688Z Perfect squares intro Factor quadratic expressions into the special products of the general form (x+a)² or (x-a)². Tomer Gal exercise https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratics-multiplying-factoring/x2f8bb11595b61c86:factor-perfect-squares/v/factoring-perfect-square-trinomials 2021-06-30T17:32:36Z Factoring perfect squares Sal factors 25x^2-30x+9 as (5x-3)^2 or as (-5x+3)^2. Sal Khan video https://cdn.kastatic.org/googleusercontent/5CcqYMA3KWSrPBPUIZtt517ekwwGim7xFbY5srOQz-sjX2oU8wcAZl9sfpgf1c2n-lp9F0kfBDeiDkPx4lPUTg Factoring perfect squares Sal factors 25x^2-30x+9 as (5x-3)^2 or as (-5x+3)^2. https://cdn.kastatic.org/ka-youtube-converted/liRNTieIU_k.mp4/liRNTieIU_k.mp4 294 Factorization through algebraic identities https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratics-multiplying-factoring/x2f8bb11595b61c86:factor-perfect-squares/e/factoring-perfect-squares 2025-02-18T07:52:09.551150445Z Perfect squares Factor quadratic expressions of the general perfect square forms: (ax)²+2abx+b² or (ax)²-2abx+b². The factored expressions have the general forms (ax+b)² or (ax-b)². Tomer Gal exercise https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratics-multiplying-factoring/x2f8bb11595b61c86:factor-perfect-squares/v/u09-l2-t1-we1-factoring-special-products-1 2021-06-30T17:32:40Z Factoring perfect squares: negative common factor Sal factors -4t^2-12t-9 as -1(2t+3)^2. Sal Khan video https://cdn.kastatic.org/googleusercontent/Nl1cABXDYkAXNM_cQMBiqnF9iPmHCtgDQ1loFqq5nsVwq-ck4N9Makwff1aq68C_Sxjo3OUXuDr04EmOdsH_AgMh Factoring perfect squares: negative common factor Sal factors -4t^2-12t-9 as -1(2t+3)^2. https://cdn.kastatic.org/ka-youtube-converted/XuwldEyWjH0.mp4/XuwldEyWjH0.mp4 232 Factorization through algebraic identities https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:poly-factor/x2ec2f6f830c9fb89:factor-w-structure/v/factoring-special-products-2 2021-06-30T17:32:40Z Factoring using the perfect square pattern Sal factors 25x^4-30x^2+9 as (5x^2-3)^2. Sal Khan video https://cdn.kastatic.org/googleusercontent/9Roa4KBS6UWgqFULhRgUDkKtGTK1pkQhUsK0kZB-BnAOgrPNecOf3-Qw8wHHu1JRXqI18gFo6JtsP4Y6yoeSzjra Factoring using the perfect square pattern Sal factors 25x^4-30x^2+9 as (5x^2-3)^2. https://cdn.kastatic.org/ka-youtube-converted/o-ZbdYVGehI.mp4/o-ZbdYVGehI.mp4 145 Factorization through algebraic identities https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratics-multiplying-factoring/x2f8bb11595b61c86:factor-perfect-squares/v/solving-for-constants-in-perfect-square-polynomial 2022-10-06T23:01:00.745424633Z Factoring perfect squares: missing values Sal analyzes the factorization of x^2+5x+c as (x+d)^2 to find the values of the missing coefficients c and d. video https://cdn.kastatic.org/ka_thumbnails_cache/05e7285c-91e3-4696-aa50-3f68d61ae805_1280_720_base.png Factoring perfect squares: missing values Sal analyzes the factorization of x^2+5x+c as (x+d)^2 to find the values of the missing coefficients c and d. https://cdn.kastatic.org/ka-youtube-converted/oIslHyWJHEY.mp4/oIslHyWJHEY.mp4 159 Factorization through algebraic identities https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:poly-factor/x2ec2f6f830c9fb89:factor-w-structure/v/factoring-difference-of-squares 2021-06-30T17:32:36Z Factoring using the difference of squares pattern If we expand (a+b)(a-b) we will get a²-b². Factorization goes the other way: suppose we have an expression that is the difference of two squares, like x²-25 or 49x²-y², then we can factor is using the roots of those squares. For example, x²-25 can be factored as (x+5)(x-5). This is an extremely useful method that is used throughout math. Sal Khan video https://cdn.kastatic.org/googleusercontent/y9jv5NuFyNqhCBTNsWtbk7jqamxFZ2aY-QAY10cnIuxvgPCCWcA03n7R-hCnHhr3VmYdJBTEJIiU3ZoXdVFLlJq_ Factoring using the difference of squares pattern If we expand (a+b)(a-b) we will get a²-b². Factorization goes the other way: suppose we have an expression that is the difference of two squares, like x²-25 or 49x²-y², then we can factor is using the roots of those squares. For example, x²-25 can be factored as (x+5)(x-5). This is an extremely useful method that is used throughout math. https://cdn.kastatic.org/ka-youtube-converted/tvnOWIoeeaU.mp4/tvnOWIoeeaU.mp4 109 Factorization through algebraic identities https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:poly-factor/x2ec2f6f830c9fb89:factor-w-structure/e/factoring_difference_of_squares_3 2026-03-17T04:40:31.334379942Z Factor polynomials using structure Factor "advanced" polynomials (i.e. polynomials of various degrees and or with two variables) using special product factorization methods. Tomer Gal exercise https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratics-multiplying-factoring/x2f8bb11595b61c86:factor-difference-squares/v/difference-of-squares-intro 2022-10-06T23:01:00.745424633Z Difference of squares intro When an expression can be viewed as the difference of two perfect squares, i.e. a²-b², then we can factor it as (a+b)(a-b). For example, x²-25 can be factored as (x+5)(x-5). This method is based on the pattern (a+b)(a-b)=a²-b², which can be verified by expanding the parentheses in (a+b)(a-b). video https://cdn.kastatic.org/ka_thumbnails_cache/c52b1b59-e0b8-4b92-931b-13024c98d84f_1280_720_base.png Difference of squares intro When an expression can be viewed as the difference of two perfect squares, i.e. a²-b², then we can factor it as (a+b)(a-b). For example, x²-25 can be factored as (x+5)(x-5). This method is based on the pattern (a+b)(a-b)=a²-b², which can be verified by expanding the parentheses in (a+b)(a-b). https://cdn.kastatic.org/ka-youtube-converted/HLNSouzygw0.mp4/HLNSouzygw0.mp4 294 Factorization through algebraic identities https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratics-multiplying-factoring/x2f8bb11595b61c86:factor-difference-squares/a/factoring-quadratics-difference-of-squares 2021-06-30T17:32:36Z Factoring quadratics: Difference of squares Learn how to factor quadratics that have the "difference of squares" form. For example, write x²-16 as (x+4)(x-4). article https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratics-multiplying-factoring/x2f8bb11595b61c86:factor-difference-squares/e/factoring_difference_of_squares_1 2025-01-15T08:58:52.349960688Z Difference of squares intro Factor quadratic expressions into the special products of the general form (x+a)(x-a). Tomer Gal exercise https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratics-multiplying-factoring/x2f8bb11595b61c86:factor-difference-squares/v/factoring-to-produce-difference-of-squares 2021-06-30T17:32:39Z Factoring difference of squares: leading coefficient ≠ 1 Sal factors 45x^2-125 as 5(3x+5)(3x-5). Sal Khan video https://cdn.kastatic.org/googleusercontent/JigOUCu1gKuO9fVWUMfTgBuU2xSrI7GhL0UHC0KCcR6nLNF8X6bEWo2cIN1ymPgJmrFqc_slHJXDiPJalNy3pio Factoring difference of squares: leading coefficient ≠ 1 Sal factors 45x^2-125 as 5(3x+5)(3x-5). https://cdn.kastatic.org/ka-youtube-converted/jmbg-DKWuc4.mp4/jmbg-DKWuc4.mp4 143 Factorization through algebraic identities https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratics-multiplying-factoring/x2f8bb11595b61c86:factor-difference-squares/v/equivalent-expressions-to-differences-of-squares 2022-10-06T23:01:00.745424633Z Factoring difference of squares: analyzing factorization Sal analyzes two different factorizations of 16x^2-64 and determines whether they are correct. video https://cdn.kastatic.org/ka_thumbnails_cache/5f125528-cff3-4f17-84c4-8ed3fa162310_1280_720_base.png Factoring difference of squares: analyzing factorization Sal analyzes two different factorizations of 16x^2-64 and determines whether they are correct. https://cdn.kastatic.org/ka-youtube-converted/TK-U1p9O6Nc.mp4/TK-U1p9O6Nc.mp4 189 Factorization through algebraic identities https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratics-multiplying-factoring/x2f8bb11595b61c86:factor-difference-squares/e/factoring_difference_of_squares_2 2025-02-13T04:57:25.728250847Z Difference of squares Factor quadratic expressions of the general difference of squares form: (ax)^2-b^2. The factored expressions have the general form (ax+b)(ax-b). Tomer Gal exercise