Câu hỏi của Ngân Ngân

Question

rút gọn: A= (a+1)^2+(b+1)^2+(c+1)^2 + 2(ab+bc+ca)-(a+b+c+1)^2

Trần Thanh Phương · Accepted Answer

$A=\left(a+1\right)^2+\left(b+1\right)^2+\left(c+1\right)^2+2\left(ab+bc+ca\right)-\left(a+b+c+1\right)^2$

$A=a^2+2a+1+b^2+2b+1+\left(c+1\right)^2+2ab+2bc+2ca-\left(a+b+c+1\right)^2$

$A=\left(a^2+2ab+b^2\right)+\left(2a+2bc+2ca+2b\right)+\left(c+1\right)^2+2-\left(a+b+c+1\right)^2$

$A=\left(a+b\right)^2+\left[2a\left(c+1\right)+2b\left(c+1\right)\right]+\left(c+1\right)^2+2-\left(a+b+c+1\right)^2$

$A=\left(a+b\right)^2+2\left(a+b\right)\left(c+1\right)+\left(c+1\right)^2+2-\left(a+b+c+1\right)^2$

$A=\left(a+b+c+1\right)^2+2-\left(a+b+c+1\right)^2$

$A=2$Câu trả lời: $A=\left(a+1\right)^2+\left(b+1\right)^2+\left(c+1\right)^2+2\left(ab+bc+ca\right)-\left(a+b+c+1\right)^2$

$A=a^2+2a+1+b^2+2b+1+\left(c+1\right)^2+2ab+2bc+2ca-\left(a+b+c+1\right)^2$

$A=\left(a^2+2ab+b^2\right)+\left(2a+2bc+2ca+2b\right)+\left(c+1\right)^2+2-\left(a+b+c+1\right)^2$

$A=\left(a+b\right)^2+\left[2a\left(c+1\right)+2b\left(c+1\right)\right]+\left(c+1\right)^2+2-\left(a+b+c+1\right)^2$

$A=\left(a+b\right)^2+2\left(a+b\right)\left(c+1\right)+\left(c+1\right)^2+2-\left(a+b+c+1\right)^2$

$A=\left(a+b+c+1\right)^2+2-\left(a+b+c+1\right)^2$

$A=2$

Bài 5: Những hằng đẳng thức đáng nhớ (Tiếp)