Question

Answer 1

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

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

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

2: \(\left(x^3-2x^2+x-1\right)\left(5-x\right)\)

\(=5x^3-x^4-10x^2+2x^3+5x-x^2-5+x\)

\(=-x^4+7x^3-11x^2+6x-5\)

3: \(\left(x^2y^2-\frac12xy+2y\right)\left(x-2y\right)\)

\(=x^3y^2-2x^2y^3-\frac12x^2y+xy^2+2xy-2y^2\)

4: \(\left(x^2-xy+y^2\right)\left(x+y\right)\)

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

\(=x^3+y^3\)