Question

Chứng minh :

a) \(\left(x-1\right)\left(x^2+x+1\right)=x^3-1\)

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

Answer 1

a.

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

ta có

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

\(=x^3-1\)

=>ĐPCM

b.

ta có

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

\(=x^4-y^4\)

=>ĐPCM

Answer 2

a, (x-1) (x² +x+1)

= x³+x²+x-x²-x-1

= x³-1 (đfcm)

b, (x³+x²y+xy²+y³) (x-y)

=x⁴+x³y+x²y²+xy³-x³y-x²y²-xy³-y⁴

= x⁴-y^{4 (đfcm)}