Answer:
4x² -4xy -4y -4
Step-by-step explanation:
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) <em>(expand)</em>
= 4x² -4xy -4x +4x -4y -4
= 4x² -4xy -4y -4
Alternatively, start by expanding the brackets.
(2x -y)² -(y +2)²
= 4x² -4xy +y² -(y² +4y +4)
= 4x² -4xy +y² -y² -4y -4 <em>(</em><em>expand</em><em>)</em>
= 4x² -4xy -4y -4 <em>(</em><em>simplify</em><em>)</em>