Question

Answer 1

a) \(\left(x^2-2x+3\right)\left(\dfrac{1}{2}x-5\right)=\dfrac{1}{2}x^3-5x^2-x^2+10x+\dfrac{3}{2}x-15\)

\(=\dfrac{1}{2}x^3+\left(-5x^2-x^2\right)+\left(10x+\dfrac{3}{2}x\right)-15\)

\(=\dfrac{1}{2}x^3-6x^2+\dfrac{23}{2}x-15\)

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

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

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

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