Question

Chứng minh rằng:

a. a³ + b³ = (a + b)³ - 3ab (a + b)

b. a³ + b³ + c³ - 3abc = (a + b + c) (a² + b² c² - ab - bc - ca)

Quang Duy, Toshiro, Hằng, Mashiro Shiina,... giúp cháu zới! *Cái này cháu đang hộ ng` ta nhé! K pải cháu đâu!

P/s: Đây là acc phụ nhóa!

Answer 1

a, Ta có:

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

Vậy..............(đpcm)

b, Ta có:

\(VT=a^3+b^3+c^3-3abc\\ =\left(a+b\right)^3-3ab\left(a+b\right)+c^3-3abc\\ =\left[\left(a+b\right)^3+c^3\right]-3ab\left(a+b\right)-3abc\\ =\left(a+b+c\right)^3-3c\left(a+b\right)\left(a+b+c\right)-3ab\left(a+b+c\right)\\ =\left(a+b+c\right)\left[\left(a+b+c\right)^2-3c\left(a+b\right)-3ab\right]\\ =\left(a+b+c\right)\left(a^2+b^2+c^2+2ab+2bc+2ac-3ac-3bc-3ab\right)\\ =\left(a+b+c\right)\left(a^2+b^2+c^2-ab-bc-ca\right)=VP\)

Vậy..............(đpcm)