Question

Tính

a/ ( x - 2 ) . ( x + 2 ) . ( x^2 + 4 ) - ( x^2 - 16 )^2

b/ ( x^3 - 5x^2 + 8x - 4 ) : ( x - 2 )

c/ ( x - y )^3 - ( x - y ) - ( x^2 + y^2 + xy )

Answer 1

a: \(\left(x-2\right)\left(x+2\right)\left(x^2+4\right)-\left(x^2-16\right)^2\)

\(=\left(x^2-4\right)\left(x^2+4\right)-\left(x^4-32x^2+256\right)\)

\(=x^4-16-x^4+32x^2-256=32x^2-272\)

b: \(\dfrac{x^3-5x^2+8x-4}{x-2}\)

\(=\dfrac{x^3-2x^2+3x^2+6x+2x-4}{x-2}\)

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

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

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