Question

Answer 1

`a)x-xy +y-y^2`

`=x(1-y)+y(1-y)`

`=(1-y)(x+y)`

`b)x^2 -4x -y^2 +4`

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

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

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

`c)x^2 - 2x -3`

`=x^2 +x -3x -3`

`=x(x+1)-3(x+1)`

`=(x+1)(x-3)`

Answer 2

\(x-xy+y-y^2=x\left(1-y\right)+y\left(1-y\right)=\left(1-y\right)\left(x+y\right)\)

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

\(x^2-2x-3=x^2+x-3x-3=x\left(x+1\right)-3\left(x+1\right)=\left(x+1\right)\left(x-3\right)\)

Answer 3

a)

\(x-xy+y-y^2\)

\(=x\left(1-y\right)+y\left(1-y\right)\)

\(=\left(1-y\right)\left(x+y\right)\)

b)

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

c)

\(x^2-2x-3=x^2-3x+x-3=x\left(x-3\right)+\left(x-3\right)=\left(x-3\right)\left(x+1\right)\)