Question

Answer 1

12) \(x^2-4xy-5y^2\)

\(=x^2-5xy+xy-5y^2\)

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

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

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

13) \(\left(x-1\right)^3-1\)

\(=\left[\left(x-1\right)-1\right]\left[\left(x-1\right)^2+\left(x-1\right)\cdot1+1^2\right]\)

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

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

Answer 2

1: =x^2-5xy+xy-5y^2

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

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

13: =(x-1)^3-1^3

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

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

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