Question

CM đẳng thức

a)(a+b) (a³ - a²b + ab² - b³)= a⁴ - b⁴

b)(a+b)(a² - ab + b²)=a³ + b³

Mọi người giúp em với

Answer 1

a) Ta có: \(VP=a^4-b^4\)

\(=\left(a^2-b^2\right)\left(a^2+b^2\right)\)

\(=\left(a+b\right)\left(a-b\right)\left(a^2+b^2\right)\)

\(=\left(a+b\right)\left(a^3+ab^2-a^2b-b^3\right)\)

\(=VT\)(đpcm)

b) Ta có: \(VT=\left(a+b\right)\left(a^2-ab+b^2\right)\)

\(=\left(a+b\right)\left(a^2+2ab+b^2-3ab\right)\)

\(=\left(a+b\right)^3-3ab\left(a+b\right)\)

\(=a^3+3a^2b+3ab^2+b^3-3a^2b-3ab^2\)

\(=a^3+b^3=VP\)(đpcm)