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Question

rút gọn biểu thức:

Q=(a+b+1)3-(a+b-1)3-6(a+b)2

Thiên Hàn · Accepted Answer

$Q=\left(a+b+1\right)^3-\left(a+b-1\right)^3-6\left(a+b\right)^2$

$Q=\left[a+b+1-a-b+1\right]\left[\left(a+b+1\right)^2+\left(a+b+1\right)\left(a+b-1\right)+\left(a+b-1\right)^2\right]-6\left(a+b\right)^2$

$Q=2\left[a^2+b^2+1+2ab+2a+2b+\left(a+b\right)^2-1+a^2+b^2+1+2ab-2a-2b\right]-6\left(a+b\right)^2$

$Q=2\left(2a^2+2b^2+4ab+1+a^2+2ab+b^2\right)-6\left(a+b\right)^2$

$Q=2\left(3a^2+3b^2+6ab+1\right)-6\left(a+b\right)^2$

$Q=2\left(3a^2+3b^2+6ab\right)+2-6\left(a+b\right)^2$

$Q=2.3\left(a^2+b^2+2ab\right)+2-6\left(a+b\right)^2$

$Q=6\left(a+b\right)^2-6\left(a+b\right)^2+2$

$Q=2$Câu trả lời: $Q=\left(a+b+1\right)^3-\left(a+b-1\right)^3-6\left(a+b\right)^2$