Question

Answer 1

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

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

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

d) \(=5\left[\left(x-y\right)^2-4z^2\right]=5\left(x-y-2z\right)\left(x-y+2z\right)\)

e) \(=\left(x-y\right)\left(x+y\right)-5\left(x-y\right)=\left(x-y\right)\left(x+y-5\right)\)

f) \(=3\left[\left(x-y\right)^2-4z^2\right]=3\left(x-y-2z\right)\left(x-y+2z\right)\)

Answer 2

\(a,=x^3+x^2+x^2+x+x+1=\left(x+1\right)\left(x^2+x+1\right)\\ b,=\left(x-2y\right)\left(x+2y\right)-2\left(x+2y\right)=\left(x+2y\right)\left(x-2y-2\right)\\ c,=x^4-2x^2+2x^3-4x+2x^2-4\\ =\left(x^2-2\right)\left(x^2+2x+2\right)\\ d,=5\left[\left(x-y\right)^2-4z^2\right]=5\left(x-y-2z\right)\left(x-y+2z\right)\\ e,=\left(x-y\right)\left(x+y\right)-5\left(x-y\right)=\left(x+y-5\right)\left(x-y\right)\\ f,=3\left[\left(x-y\right)^2-4z^2\right]=3\left(x-y-2z\right)\left(x-y+2z\right)\)

Answer 3

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

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

c: \(=\left(x^2-2\right)\cdot\left(x^2+2\right)+2x\left(x^2-2\right)\)

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