Question

Answer 1

a) \(x^3-4x^2+4x=x\left(x^2-4x+4\right)=x\left(x-2\right)^2\)

b) \(x^2-y^2-6y-9=x^2-\left(y^2+6y+9\right)=x^2-\left(y+3\right)^2=\left(x+y+3\right)\left(x-y-3\right)\)

c) \(3x^2+x-4=\left(3x^2-3x\right)+\left(4x-4\right)=3x\left(x-1\right)+4\left(x-1\right)=\left(3x+4\right)\left(x-1\right)\)

Answer 2

a)

\(x^3-4x^2+4x=x\left(x^2-4x+4\right)=x\left(x-2\right)^2\)

b)\(x^2-y^2-6y-9=-\left(y^2+6y+9\right)+x^2=-\left(y+3\right)^2+x^2=\left(y+3\right)^2-x^2=\left(y+3-x\right)\left(y+3+x\right)\)