Câu hỏi của Bui Trinh Minh Ngoc

Question

1.Phân tích đa thức sau thành nhân tử:a,x2(y-z)+y2(z-x)+z2(x-y)giải chi tiết nha!Mk cần gấp lắm!!!!!!!!!!

ST · Accepted Answer

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

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