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1/ \(\left(a-b\right)\left(a^2+3ab+b^2\right)+\left(a+b\right)^3+ab\left(b-a\right)=\left(a^2+2ab+b^2+ab\right)\left(a-b\right)+\left(a+b\right)^3+ab\left(b-a\right)\)= \(\left(a^2+2ab+b^2\right)\left(a-b\right)+\left(a+b\right)ab+\left(a-b\right)^3-ab\left(a-b\right)\)
= \(\left(a+b\right)^2\left(a-b\right)+\left(a+b\right)^3\)
= \(\left(a+b\right)^2\left(a-b+a+b\right)=2a\left(a+b\right)^2\)
k mình nhé!
1, \(a^2b-2ab^2+ab\) = \(ab\left(a-2b+1\right)\)
2, \(a\left(x-1\right)+b\left(1-x\right)\)=\(a\left(x-1\right)-b\left(x-1\right)\)
=\(\left(x-1\right)\left(a-b\right)\)
1,
\(a,7x-6x^2-2=-6x^2+7x-2=-6x^2+3x+4x-2\)
\(=-3x\left(2x-1\right)+2\left(2x-1\right)=\left(2x-1\right)\left(2-3x\right)\)
\(b,2x^2+3x-5=2x^2-2x+5x-5\)
\(=2x\left(x-1\right)+5\left(x-1\right)=\left(x-1\right)\left(2x+5\right)\)
\(c,16x-5x^2-3=-5x^2+x+15x-3\)
\(=-x\left(5x-1\right)+3\left(5x-1\right)=\left(5x-1\right)\left(3-x\right)\)
2,
\(a+b+c=0=>a+b=-c=>\left(a+b\right)^3=\left(-c\right)^3\)
\(=>a^3+b^3+3a^2b+3ab^2=-c^3\)
\(=>a^3+b^3+c^3=-3ab\left(a+b\right)\)
\(=>a^3+b^3+c^3=-3ab\left(-c\right)=3abc\)(vì a+b=-c)
\(2x^2+3x-5\)
\(=2x^2-2x+5x-5\)
\(=2x\left(x-1\right)+5\left(x-1\right)\)
\(=\left(x-1\right)\left(2x+5\right)\)