Question

a) x^2 - 4x + 4 - y^2          

b) x^2 + 2xy + y^2 - 2x - 2y

 

Answer 1

a)\(=\left(x^2-4x+4\right)-y^2=\left(x-2\right)^2-y^2=\left(x-2-y\right)\left(x-2+y\right)=\left(x-y-2\right)\left(x+y-2\right)\)

Answer 2

b) \(=\left(x^2+2xy+y^2\right)-\left(2x+2y\right)=\left(x+y\right)^2-2\left(x+y\right)=\left(x+y\right)\left(x+y-2\right)\)

Answer 3

a) $x^2-4x+4-y^2$

$=x^2-2.x.2+2^2-y^2$

$=(x-2)^2-y^2$

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

b) $x^2 + 2xy + y^2 - 2x - 2y$

$=x^2+2.x.y+y^2-2x-2y$

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

$=(x+y)^2+2(x+y)$

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