Question

Answer 1

a: =(x^2-1)^2

=(x-1)^2*(x+1)^2

b: =(x-y)*(x+y)+5(x-y)

=(x-y)(x+y+5)

c: =y^2-(2x-1)^2

=(y-2x+1)(y+2x-1)

d: =(x+2)^2(x^3-1)-(x^3-1)

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

=(x-1)(x^2+x+1)(x+1)(x+3)

Answer 2

a)

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

b)

\(=\left(x^2-y^2\right)-\left(5x-5y\right)\)

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

c)

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

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

d)

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

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

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

\(=\left(x-1\right)\left(x^2+x+1\right)\left(x^2+2x+5\right)\)