Question

1.

a) y^2(x+y)-zx-zy

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

c) x^2+x-y^2+y

d) x^3+x^2+x+1

Answer 1

a) \(y^2\left(x+y\right)-zx-zy\)

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

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

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

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

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

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

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

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

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

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

d) \(x^3+x^2+x+1\)

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

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