Câu hỏi của Kaori Miyazono

Question

Phân tích đa thức thành nhân tử :a) $\left(x^2+y^2\right)^3+\left(z^2-x^2\right)^3-\left(y^2+z^2\right)^3$b)$\left(x+y\right)^3-x^3-y^3$c)$\left(x+y+z\right)^3-x^3-y^3-z^3$

Dương Lam Hàng · Accepted Answer

a) $\left(x^2+y^2\right)^3+\left(z^2-x^2\right)^3-\left(y^2+z^2\right)^3$$=\left[\left(x^2+y^2\right)^3+\left(z^2-x^2\right)^3\right]-\left(y^2+z^2\right)^3$$=\left(x^2+y^2+z^2-x^2\right)\left[\left(x^2+y^2\right)^2-\left(x^2+y^2\right)\left(z^2-x^2\right)+\left(z^2-x^2\right)^2\right]-\left(y^2+z^2\right)^3$$=\left(y^2+z^2\right)\left(x^4+2x^2y^2+y^4-x^2z^2+x^4-y^2z^2+x^2y^2+z^4-2z^2x^2+x^4\right)-\left(y^2+z^2\right)^3$$=\left(y^2+z^2\right)\left[x^4+2x^2y^2+y^4-x^2z^2+x^4-y^2z^2+x^2y^2+z^4-2z^2x^2+x^4-\left(y^2+z^2\right)^2\right]$$=\left(y^2+z^2\right)\left(x^4+2x^2y^2+y^4-x^2z^2+x^4-y^2z^2+x^2y^2+z^4-2z^2x^2+x^4-y^4-2y^2z^2-z^4\right)$$=\left(y^2+z^2\right)\left(3x^4+3x^2y^2-3x^2z^2-3y^2z^2\right)$   = 3(y2+z2)(x4+x2y2-x2z2-y2z2)   = 3(y2+z2)[x2(x2+y2)-z2(x2+y2)]   = 3(y2+z2)(x2-z2)(x2+y2)   = 3(y2+z2)(x-z)(x+z)(x2+y2)b) $\left(x+y\right)^3-x^3-y^3$$=x^3+3x^2y+3xy^2+y^3-x^3-y^3$$=3x^2y+3xy^2=3xy\left(x+y\right)$c) $\left(x+y+z\right)^3-x^3-y^3-z^3$$=\left[\left(x+y\right)+z\right]^3-x^3-y^3-z^3$$=\left(x+y\right)^3+3\left(x+y\right)^2.z+3\left(x+y\right).z^2+z^3-x^3-y^3-z^3$$=\left(x+y\right)^3+3\left(x+y\right)^2.z+3\left(x+y\right).z^2-\left(x^3+y^3\right)$$=\left(x+y\right)\left[\left(x+y\right)^2+3\left(x+y\right).z+3z^2\right]-\left(x+y\right)\left(x^2-xy+y^2\right)$$=\left(x+y\right)\left(x^2+2xy+y^2+3xz+3yz+3z^2-x^2+xy-y^2\right)$  = (x+y)[3xy+3xz+3yz+3z2 ]   = 3(x+y)(xy+xz+yz+z2)  = 3(x+y)[x(y+z)+z(y+z)]  = 3(x+y)(x+z)(y+z)Câu trả lời: a) $\left(x^2+y^2\right)^3+\left(z^2-x^2\right)^3-\left(y^2+z^2\right)^3$$=\left[\left(x^2+y^2\right)^3+\left(z^2-x^2\right)^3\right]-\left(y^2+z^2\right)^3$$=\left(x^2+y^2+z^2-x^2\right)\left[\left(x^2+y^2\right)^2-\left(x^2+y^2\right)\left(z^2-x^2\right)+\left(z^2-x^2\right)^2\right]-\left(y^2+z^2\right)^3$$=\left(y^2+z^2\right)\left(x^4+2x^2y^2+y^4-x^2z^2+x^4-y^2z^2+x^2y^2+z^4-2z^2x^2+x^4\right)-\left(y^2+z^2\right)^3$$=\left(y^2+z^2\right)\left[x^4+2x^2y^2+y^4-x^2z^2+x^4-y^2z^2+x^2y^2+z^4-2z^2x^2+x^4-\left(y^2+z^2\right)^2\right]$$=\left(y^2+z^2\right)\left(x^4+2x^2y^2+y^4-x^2z^2+x^4-y^2z^2+x^2y^2+z^4-2z^2x^2+x^4-y^4-2y^2z^2-z^4\right)$$=\left(y^2+z^2\right)\left(3x^4+3x^2y^2-3x^2z^2-3y^2z^2\right)$   = 3(y2+z2)(x4+x2y2-x2z2-y2z2)   = 3(y2+z2)[x2(x2+y2)-z2(x2+y2)]   = 3(y2+z2)(x2-z2)(x2+y2)   = 3(y2+z2)(x-z)(x+z)(x2+y2)b) $\left(x+y\right)^3-x^3-y^3$$=x^3+3x^2y+3xy^2+y^3-x^3-y^3$$=3x^2y+3xy^2=3xy\left(x+y\right)$c) $\left(x+y+z\right)^3-x^3-y^3-z^3$$=\left[\left(x+y\right)+z\right]^3-x^3-y^3-z^3$$=\left(x+y\right)^3+3\left(x+y\right)^2.z+3\left(x+y\right).z^2+z^3-x^3-y^3-z^3$$=\left(x+y\right)^3+3\left(x+y\right)^2.z+3\left(x+y\right).z^2-\left(x^3+y^3\right)$$=\left(x+y\right)\left[\left(x+y\right)^2+3\left(x+y\right).z+3z^2\right]-\left(x+y\right)\left(x^2-xy+y^2\right)$$=\left(x+y\right)\left(x^2+2xy+y^2+3xz+3yz+3z^2-x^2+xy-y^2\right)$  = (x+y)[3xy+3xz+3yz+3z2 ]   = 3(x+y)(xy+xz+yz+z2)  = 3(x+y)[x(y+z)+z(y+z)]  = 3(x+y)(x+z)(y+z)

KAl(SO4)2·12H2O · Answer

a) $\left(x^2+y^2\right)^3+\left(z^2-x^3\right)-\left(y^2+z^2\right)^3$$=x^6+3x^4y^2+3x^4y^2+y^6+z^2+-x^2+-y^6+-3y^4z+-3y^2z^4+-z^6$$=x^6+3x^4y^2+3x^2y^4+-3y^4z^4+-z^6+-x^2+z^2$b) $\left(x+y\right)^3-x^3-y^3$$=x^3+3x^2y+3xy^2+y^3+-x^3+-y^3$$=\left(x^3+-x^3\right)+\left(3x^2y\right)+\left(3xy^2\right)+\left(y^3+-y^3\right)$$=3x^2y+3xy^2$c) $\left(x+y+z\right)^3-x^3-y^3-z^3$$=x^3+3x^2y+3x^2z+3xy^2+6xyz+3xz^2+y^3+3y^2z+3yz^2+z^2-x^3-y^3-z^3$$=3x^2y+3x^2z+3xy^2+3xy^2+6xyz+3xz^2+3y^2z+3yz^2$P/s: Ko chắcCâu trả lời: a) $\left(x^2+y^2\right)^3+\left(z^2-x^3\right)-\left(y^2+z^2\right)^3$$=x^6+3x^4y^2+3x^4y^2+y^6+z^2+-x^2+-y^6+-3y^4z+-3y^2z^4+-z^6$$=x^6+3x^4y^2+3x^2y^4+-3y^4z^4+-z^6+-x^2+z^2$b) $\left(x+y\right)^3-x^3-y^3$$=x^3+3x^2y+3xy^2+y^3+-x^3+-y^3$$=\left(x^3+-x^3\right)+\left(3x^2y\right)+\left(3xy^2\right)+\left(y^3+-y^3\right)$$=3x^2y+3xy^2$c) $\left(x+y+z\right)^3-x^3-y^3-z^3$$=x^3+3x^2y+3x^2z+3xy^2+6xyz+3xz^2+y^3+3y^2z+3yz^2+z^2-x^3-y^3-z^3$$=3x^2y+3x^2z+3xy^2+3xy^2+6xyz+3xz^2+3y^2z+3yz^2$P/s: Ko chắc

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