(x-2y)^2-4(x-2y)y+4y^2

less than a minute read Jun 17, 2024

Factoring the Expression (x - 2y)^2 - 4(x - 2y)y + 4y^2

This expression appears to be a perfect square trinomial, which means it can be factored into the square of a binomial. Let's break down the process:

1. Recognize the Pattern:

First term: (x - 2y)^2 is a perfect square
Last term: 4y^2 is also a perfect square (2y)^2
Middle term: -4(x - 2y)y is twice the product of the square roots of the first and last terms.

2. Factor the Expression:

Based on the pattern, we can factor the expression as follows:

(x - 2y)^2 - 4(x - 2y)y + 4y^2 = [(x - 2y) - 2y]^2

3. Simplify:

Simplifying the expression further, we get:

[(x - 2y) - 2y]^2 = (x - 4y)^2

Therefore, the factored form of the expression (x - 2y)^2 - 4(x - 2y)y + 4y^2 is (x - 4y)^2.