Question

(2х + 3у)2 - (2х – 5у)2.

Answer 1

Ответ:

Пошаговое объяснение:

(2х + 3у)2 - (2х – 5у)2

4x+6y-(4x-10y)

4x+6y-4x+10y

Ответ:16y

Answer 2

To simplify the given expression $(2x + 3y)^2 - (2x - 5y)^2$, we can use the identity $a^2 - b^2 = (a + b)(a - b)$. Let's apply this identity to simplify the expression step by step:

1. Expand $(2x + 3y)^2$:

   $$(2x + 3y)^2 = (2x + 3y)(2x + 3y) = 4x^2 + 12xy + 9y^2$$

2. Expand $(2x - 5y)^2$:

   $$(2x - 5y)^2 = (2x - 5y)(2x - 5y) = 4x^2 - 20xy + 25y^2$$

3. Substitute the expanded expressions into the original expression and apply the $a^2 - b^2 = (a + b)(a - b)$ identity:

   $$(4x^2 + 12xy + 9y^2) - (4x^2 - 20xy + 25y^2) \\ = 4x^2 + 12xy + 9y^2 - 4x^2 + 20xy - 25y^2 \\ = 32xy - 16y^2$$

So, $(2x + 3y)^2 - (2x - 5y)^2 = 32xy - 16y^2$.