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Question

Phân tích thành nhân tử: x^2(y-z)+y^2(z-x)+z^2(x-y)

alibaba nguyễn · Accepted Answer

x2(y - z) + y2(z - x) + z2(x - y)= z2(x - y) + x2 y - x2 z + y2 z - y2 x= z2(x - y) + (x2 y  - y2 x) + (- x2 z + y2 z)= (x - y)(z2 + xy - zx - zy)= (x - y)[(z2 - zx) + (xy - zy)]= (x - y)(z - x)(z -y)Câu trả lời: x2(y - z) + y2(z - x) + z2(x - y)= z2(x - y) + x2 y - x2 z + y2 z - y2 x= z2(x - y) + (x2 y  - y2 x) + (- x2 z + y2 z)= (x - y)(z2 + xy - zx - zy)= (x - y)[(z2 - zx) + (xy - zy)]= (x - y)(z - x)(z -y)

oOo Lê Việt Anh oOo · Answer

$x^2\left(y-z\right)+y^2\left(z-x\right)+z^2\left(x-y\right)$$=x^2\left(y-z\right)+y^2\left(z-y+y-x\right)$$=x^2\left(y-z\right)-y^2\left(y-z\right)-y^2\left(x-y\right)+z^2\left(x-y\right)$$=\left(x-y\right)\left(x+y\right)\left(y-z\right)+\left(z-y\right)\left(y+z\right)\left(x-y\right)$$=\left(x-y\right)\left(y-x\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)$$=x^2\left(y-z\right)+y^2\left(z-y+y-x\right)$$=x^2\left(y-z\right)-y^2\left(y-z\right)-y^2\left(x-y\right)+z^2\left(x-y\right)$$=\left(x-y\right)\left(x+y\right)\left(y-z\right)+\left(z-y\right)\left(y+z\right)\left(x-y\right)$$=\left(x-y\right)\left(y-x\right)\left(x-z\right)$

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