Question

Phân tích nhân tử:

a)4x²yz-8xy²z+12xyz²

b)y²(a-b)+b-a

c)8m²(m-n)+10(n-m)²

d)3x(a-2b)²-(x-2)(2b-a)²

e)5a(x-y)³-(a+4)(y-x)³

Answer 1

\(a,4x^2yz-8xy^2z+12xyz^2\)\(=4xyz\left(x-8y+12z\right)\)\(b,y^2\left(a-b\right)+b-a\)\(=y^2\left(a-b\right)+\left(b-a\right)\)\(=y^2\left(a-b\right)-\left(a-b\right)\)\(=\left(a-b\right)\left(y^2-1\right)\)\(c,8m^2\left(m-n\right)+10\left(n-m\right)^2\)\(=8m^2\left(m-n\right)+10\left(m-n\right)^2\)\(=\left(m-n\right)\left(8m^2+10\left(m-n\right)\right)\)\(d,3x\left(a-2b\right)^2-\left(x-2\right)\left(2b-a\right)^2\)\(=3x\left(a-2b\right)^2-\left(x-2\right)\left(a-2b\right)^2\)\(=\left(a-2b\right)^2\left(3x-x+2\right)\)\(e,5a\left(x-y\right)^3-\left(a+4\right)\left(y-x\right)^3\)\(=5a\left(x-y\right)^3-\left(a+4\right)\left(x-y\right)^3\)\(=\left(x-y\right)^3\left(5a-a-4\right)\)

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