Câu hỏi của Nguyễn Phi Nhung

Question

(a - b) 3 + (b - c)3 + (c - a)3

Nguyễn Việt Lâm · Accepted Answer

$\left(a-b\right)^3+\left(b-c\right)^3+\left(c-a\right)^3$

$=\left(a-c\right)\left(a^2-3ab+3b^2-3bc+c^2+ac\right)-\left(a-c\right)^3$

$=\left(a-c\right)\left(a^2-3ab+3b^2-3bc+c^2+ac-a^2+2ac-c^2\right)$

$=\left(a-c\right)\left(3b^2-3ab-3bc+3ac\right)$

$=3\left(a-c\right)\left[b\left(b-a\right)-c\left(b-a\right)\right]$

$=3\left(a-c\right)\left(b-c\right)\left(b-a\right)$Câu trả lời: $\left(a-b\right)^3+\left(b-c\right)^3+\left(c-a\right)^3$

$=\left(a-c\right)\left(a^2-3ab+3b^2-3bc+c^2+ac\right)-\left(a-c\right)^3$

$=\left(a-c\right)\left(a^2-3ab+3b^2-3bc+c^2+ac-a^2+2ac-c^2\right)$

$=\left(a-c\right)\left(3b^2-3ab-3bc+3ac\right)$

$=3\left(a-c\right)\left[b\left(b-a\right)-c\left(b-a\right)\right]$

$=3\left(a-c\right)\left(b-c\right)\left(b-a\right)$

Bài 3: Những hằng đẳng thức đáng nhớ