Phân tích đa thức thành nhân tử:
a) \(\left(a+b\right)+\left(a+b\right)^2\)
b) \(4\left(x-y\right)+3\left(x-y\right)^2\)
c) \(\left(a-b\right)+\left(b-a\right)^2\)
d) \(\left(a-b\right)-\left(b-a\right)^2\)
e) \(a\left(a-b\right)^2-\left(b-a\right)^3\)
f) \(\left(y+z\right)\left(12x^2+6x\right)+\left(y-z\right)\left(12x^2+6x\right)\)
\(a,\left(a+b\right)+\left(a+b\right)^2\)
\(=\left(a+b\right)\left(1+a+b\right)\)
\(b,4\left(x-y\right)+3\left(x-y\right)^2\)
\(=\left(x-y\right)\left(4+3\left(x-y\right)\right)\)
\(=\left(x-y\right)\left(4+3x-3y\right)\)
\(c,\left(a-b\right)+\left(b-a\right)^2\)
\(=\left(a-b\right)+\left(a-b\right)^2\)
\(=\left(a-b\right)\left(1+a-b\right)\)
a) \(\left(a+b\right)+\left(a+b\right)^2=\left(a+b\right)\left(1+a+b\right)\)
b) \(4\left(x-y\right)+3\left(x-y\right)^2=\left(x-y\right)\left[4+3.\left(x-y\right)\right]\)
c) \(\left(a-b\right)+\left(b-a\right)^2=\left(a-b\right)+\left(b-a\right)\left(b-a\right)\)
\(=\left(a-b\right)-\left(a-b\right)\left(b-a\right)\)
\(=\left(a-b\right)\left(1-b+a\right)\)
d) \(\left(a-b\right)-\left(b-a\right)^2\)
\(=\left(a-b\right)-\left(b-a\right)\left(b-a\right)\)
\(=\left(a-b\right)+\left(a-b\right)\left(b-a\right)\)
\(=\left(a-b\right)\left(1+b-a\right)\)
e) \(a\left(a-b\right)^2-\left(b-a\right)^3\)
\(=a\left(a-b\right)-\left(a-b\right)\left(b-a\right)^2\)
\(=\left(a-b\right)\left[a-\left(b-a\right)^2\right]\)
f) \(\left(y+z\right)\left(12x^2+6x\right)+\left(y-z\right)\left(12x^2+6x\right)\)
\(=\left(12x^2+6x\right)\left(y+z+y-z\right)\)
\(=\left(12x^2+6x\right)2y\)