Question

(2x–y)²–(y+2)²-----------

Answer 1

4x² -4xy -4y -4

Explanation:

`\boxed{ {a}^(2) - {b}^(2) = (a + b)(a - b)}`

In this case, a= 2x -y and b= y +2.

(2x -y)² -(y +2)²

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

= (2x +2)(2x -y -y -2)

= (2x +2)(2x -2y -2)

= 2x(2x) +2x(-2y) +2x(-2) +2(2x) +2(-2y) +2(-2) (expand)

= 4x² -4xy -4x +4x -4y -4

= 4x² -4xy -4y -4

Alternatively, start by expanding the brackets.

`\boxed{(a - b)^(2) = {a}^(2) - 2ab \: + {b}^(2) }`

`\boxed{(a + b)^(2) = {a}^(2) + 2ab \: + {b}^(2) }`

(2x -y)² -(y +2)²

= 4x² -4xy +y² -(y² +4y +4)

= 4x² -4xy +y² -y² -4y -4 (expand)

= 4x² -4xy -4y -4 (simplify)