Question

Answer 1

a)

\(=\left(8x^3-1\right)-\left(12x^2-6x\right)=\left(2x-1\right)\left(4x^2+2x+1\right)-6x\left(2x-1\right)=\left(2x-1\right)\left(4x^2+2x+1-6x\right)=\left(2x-1\right)\left(4x^2-4x+1\right)=\left(2x-1\right)\left(2x-1\right)^2=\left(2x-1\right)^3\)

b)

\(=x^3+3\cdot x^2\cdot2y+3\cdot x\cdot4y^2+\left(2y\right)^3+y^3=\left(x+2y\right)^3+y^3=\left(x+2y+y\right)\left[\left(x+2y\right)^2-\left(x+2y\right)\cdot y+y^2\right]=\left(x+3y\right)\left(x^2+4y+4y^2-xy-2y^2+y^2\right)=\left(x+3y\right)\left(x^2-xy+4y+3y^2\right)\)

 

 

Answer 2