Question

Tinh

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

b) \(\left(x+3\right).\left(x^2-3x+9\right)-x.\left(x-2\right).\left(x+2\right)\)

 

Answer 1

a)

Ta có :

\(\left(x+y\right)^3+\left(y-x\right)^3\)

\(=\left(x+y+y-x\right)\left[\left(x+y\right)^2-\left(x+y\right)\left(y-x\right)+\left(y-x\right)^2\right]\)

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

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

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

b) Ta có :

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

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

\(=x^3-x^2+\left(27-4\right)\)

\(=x^3-x^2-23\)