Câu hỏi của Luong Thi Kim Oanh

Question

Phân tích đa thức thành nhân tử :( x - y )3 + ( y - z )3 + ( z - x )3ai nhanh mk tích cho !!!

ST · Accepted Answer

$=\left(x-y+y-z\right)\left[\left(x-y\right)^2-\left(x-y\right)\left(y-z\right)+\left(y-z\right)^2\right]-\left(x-z\right)^2$$=\left(x-z\right)\left[\left(x-y\right)\left(x-y-y+z\right)+\left(y-z\right)^2-\left(x-z\right)^2\right]$$=\left(x-z\right)\left[\left(x-y\right)\left(x-2y+z\right)+\left(y-z-x+z\right)\left(y-z+x-z\right)\right]$$=\left(x-z\right)\left[\left(x-y\right)\left(x-2y+z\right)-\left(x-y\right)\left(x+y-2z\right)\right]$$=\left(x-z\right)\left(x-y\right)\left(x-2y+z-x-y+2z\right)$$=\left(x-z\right)\left(x-y\right)\left(-3y+3z\right)$$=-3\left(x-y\right)\left(x-z\right)\left(y-z\right)$Câu trả lời: $=\left(x-y+y-z\right)\left[\left(x-y\right)^2-\left(x-y\right)\left(y-z\right)+\left(y-z\right)^2\right]-\left(x-z\right)^2$$=\left(x-z\right)\left[\left(x-y\right)\left(x-y-y+z\right)+\left(y-z\right)^2-\left(x-z\right)^2\right]$$=\left(x-z\right)\left[\left(x-y\right)\left(x-2y+z\right)+\left(y-z-x+z\right)\left(y-z+x-z\right)\right]$$=\left(x-z\right)\left[\left(x-y\right)\left(x-2y+z\right)-\left(x-y\right)\left(x+y-2z\right)\right]$$=\left(x-z\right)\left(x-y\right)\left(x-2y+z-x-y+2z\right)$$=\left(x-z\right)\left(x-y\right)\left(-3y+3z\right)$$=-3\left(x-y\right)\left(x-z\right)\left(y-z\right)$

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