https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:poly-factor/x2ec2f6f830c9fb89:factor-w-structure/v/id-quad-patterns 2023-08-25T18:29:21.068066409Z Identifying quadratic patterns Factoring using structure involves recognizing patterns in expressions, like the difference of squares or perfect square trinomials, and using these patterns to break down complex expressions into simpler ones. As an example, you’ll determine whether the polynomial 9x⁸+6x⁴y+y² can be factored using the perfect square pattern or the difference of squares pattern (or neither). video https://cdn.kastatic.org/googleusercontent/B-vHSqs4-cNIVKRRnWLKheEb3GDBlBB8pHGNs-Y6vUU-HAgGKgWQRP6LIA3q6-00YYjOv2jvgZJrfInev9CiJXrj Identifying quadratic patterns Factoring using structure involves recognizing patterns in expressions, like the difference of squares or perfect square trinomials, and using these patterns to break down complex expressions into simpler ones. As an example, you’ll determine whether the polynomial 9x⁸+6x⁴y+y² can be factored using the perfect square pattern or the difference of squares pattern (or neither). https://cdn.kastatic.org/ka-youtube-converted/OcavJJA8Uyg.mp4/OcavJJA8Uyg.mp4 350 Factoring using structure https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:poly-factor/x2ec2f6f830c9fb89:factor-w-structure/e/identify-quadratic-patterns 2021-07-29T22:44:48.94944018Z Identify quadratic patterns Given a polynomial expression whose degree is more than 2, determine whether it can be factored using one of the common quadratic patterns. Tomer Gal exercise https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:poly-factor/x2ec2f6f830c9fb89:factor-w-structure/v/factor-w-substitution 2023-08-25T18:29:21.068066409Z Factorization with substitution Unravel the mystery of algebraic expressions with factorization using substitution! This lesson explores how to simplify complex expressions by identifying patterns and substituting variables. By using U+V² and U+V x U-V structures, you can easily transform and factor expressions! video https://cdn.kastatic.org/googleusercontent/Gu4DCS41lvxUDHpA6_mrZQmLw4iMApI60MFZf9vs0KJge6d1L_qlRo8GHWRwPYm5ROgIXoABMqVCWeBxF9R3Hbt- Factorization with substitution Unravel the mystery of algebraic expressions with factorization using substitution! This lesson explores how to simplify complex expressions by identifying patterns and substituting variables. By using U+V² and U+V x U-V structures, you can easily transform and factor expressions! https://cdn.kastatic.org/ka-youtube-converted/js5cP-rq0FI.mp4/js5cP-rq0FI.mp4 313 Factoring using structure https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:poly-factor/x2ec2f6f830c9fb89:factor-w-structure/e/factorization-with-substitution 2021-08-12T16:00:39.880213098Z Factorization with substitution Given a polynomial expression whose degree is more than 2, determine the necessary substitution in order to factor it using one of the common quadratic patterns. Tomer Gal exercise 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 Factoring using structure 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 Factoring using structure 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