Question

2/ Thực hiện phép tính

a/ (x-y)(x²+xy+y²)

b/(x²-2xy+y²)(x-y)

c/ (x²y²-\(\dfrac{1}{3}\) xy+3y)(x-3y)

d/(\(\dfrac{1}{5}\)x-1)(x² -5x+2)

Answer 1

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

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

c ) \(\left(x^2y^2-\dfrac{1}{3}xy+3y\right)\left(x-3y\right)\)

\(=\left(x^2y^2-\dfrac{1}{3}xy+3y\right)x-3y\left(x^2y^2-\dfrac{1}{3}xy+3y\right)\)

\(=x^3y^2-\dfrac{1}{3}x^2y+3xy-3x^2y^3+xy^2-9y^2\)

d ) \(\left(\dfrac{1}{5}x-1\right)\left(x^2-5x+2\right)\)

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

\(=\dfrac{1}{5}x^3-x^2+\dfrac{2}{5}x-x^2+5x-2\)

\(=\dfrac{1}{5}x^3-2x^2+\dfrac{27}{5}x-2\)

Answer 2

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