Question

Answer 1

a) \(\left(x-2\right)\left(6x^2-5x+1\right)\)

\(=6x^3-5x^2+5x-12x^2+10x-2\)

\(=6x^3-17x^2+15x-2\)

b) \(\left(x-2y\right)\cdot\left(x^2y^2-xy+2y\right)\)

\(=x^3y^2-x^2y+2xy-2x^2y^3-2xy^2-4y^2\)

c) \(\left(x+3\right)\left(x^2+3x-5\right)\)

\(=x^3+3x^2-5x+3x^2+9x-15\)

\(=x^3+6x^2+4x-15\)

Answer 2

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

f) \(\left(x-y\right)\left(x^2+xy+y^2\right)=x^3-y^3\)

g) \(\left(x^2-xy+y^2\right)\left(x+y\right)=x^3-y^3\)

h) \(\left(x^2-3x+9\right)\left(x+3\right)=x^3+27\)