phân tích đa thức thành nhân tử (x+y)(x2-y2)+(y+z)(y2-z2)+(z+x)(z2-x2)
K
Khách
Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
Những câu hỏi liên quan
CM
13 tháng 10 2017
x 2 y + x y 2 + x 2 z + x z 2 + y 2 z + y z 2 + 3xyz.
= ( x 2 y + x 2 z + xyz) + (x y 2 + y 2 z + xyz) + (x z 2 + y z 2 + xyz)
= x(xy + xz + yz) + y(xy + yz + xz) + z(xz + yz + xy)
= (x + y + z)(xy + xz + yz).
NC
14 tháng 12 2020
\(x^2y+xy^2+x^2z+xz^2+y^2z+yz^2+3xyz\)
\(=\left(x^2y+x^2z+xyz\right)+\left(xz^2+yz^2+xyz\right)+\left(xy^2+y^2z+xyz\right)\)
\(=x\left(xy+xz+yz\right)+z\left(xz+yz+xy\right)+y\left(xy+yz+xz\right)\)
\(=\left(x+y+z\right)\left(xy+yz+xz\right)\)
PT
1
TL
1
23 tháng 8 2021
\(A=x\left(y^2-z^2\right)+y\left(z^2-x^2\right)+z\left(x^2-y^2\right)=x\left(y^2-z^2\right)+y\left(-y^2+z^2-x^2+y^2\right)+z\left(x^2-y^2\right)=\left(y^2-z^2\right)\left(x-y\right)+\left(x^2-y^2\right)\left(z-y\right)=\left(y-z\right)\left(y+z\right)\left(x-y\right)-\left(x-y\right)\left(x+y\right)\left(y-z\right)=\left(x-y\right)\left(y-z\right)\left(y+z-x-y\right)=\left(x-y\right)\left(y-z\right)\left(z-x\right)\)
23 tháng 8 2021
\(B=a\left(b^3-c^3\right)+b\left(c^3-a^3\right)+c\left(a^3-b^3\right)=ab^3-ac^3+bc^3-a^3b+a^3c-b^3c=ab\left(b^2-a^2\right)-c^3\left(a-b\right)+c\left(a^3-b^3\right)=-ab\left(a-b\right)\left(a+b\right)-c^3\left(a-b\right)+c\left(a-b\right)\left(a^2+ab+b^2\right)=\left(a-b\right)\left(-a^2b-ab^2-c^3+a^2c+abc+b^2c\right)\)
NT
0
HT
2
25 tháng 8 2021
a: Ta có: \(x^2-xy-3x+3y\)
\(=x\left(x-y\right)-3\left(x-y\right)\)
\(=\left(x-y\right)\left(x-3\right)\)
b: Ta có: \(5x^2+5xy-x-y\)
\(=5x\left(x+y\right)-\left(x+y\right)\)
\(=\left(x+y\right)\left(5x-1\right)\)
c: Ta có: \(x^2-2xy+y^2-z^2\)
\(=\left(x-y\right)^2-z^2\)
\(=\left(x-y-z\right)\left(x-y+z\right)\)
MH
25 tháng 10 2021
a) \(3x\left(2x-y\right)+5y\left(y-2x\right)\)
\(=3x\left(2x-y\right)-5y\left(2x-y\right)\)
\(=\left(3x-5y\right)\left(2x-y\right)\)
b) \(\left(x-5\right)^2-9\left(x+y\right)^2\)
\(=\left(x-5\right)^2-3^2\left(x+y\right)^2\)
\(=\left(x-5\right)^2-\left(3x+3y\right)^2\)
\(=\left(x-5+3x+3y\right)\left(x-5-3x-3y\right)\)
\(=\left(4x+3y-5\right)\left(-2x-3y-5\right)\)
25 tháng 10 2021
a: \(3x\left(2x-y\right)+5y\left(y-2x\right)=\left(2x-y\right)\left(3x-5y\right)\)
e: \(x^2-10x+24=\left(x-4\right)\left(x-6\right)\)
Ta có :
\(\left(x+y\right)\left(x^2-y^2\right)+\left(y+z\right)\left(y^2-z^2\right)+\left(z+x\right)\left(z^2-x^2\right)\)
\(=\left(x+y\right)^2.\left(x-y\right)+\left(y+z\right).\left(y^2-x^2+x^2-z^2\right)+\left(z+x\right)\left(z^2-x^2\right)\)
\(=\left(x+y\right)\left(x^2-y^2\right)-\left(y+z\right)\left(x^2-y^2+z^2-x^2\right)+\left(z+x\right)\left(z^2-x^2\right)\)
\(=\left(x+y\right)\left(x^2-y^2\right)-\left(y+z\right)\left(x^2-y^2\right)-\left(y+z\right)\left(z^2-x^2\right)+\left(z+x\right)\left(z^2-x^2\right)\)
\(=\left(x^2-y^2\right)\left(x+y-y-z\right)-\left(z^2-x^2\right).\left(y+z-z-x\right)\)
\(=\left(x^2-y^2\right).\left(x-z\right)-\left(z^2-x^2\right).\left(y-x\right)\)
\(=\left(x-y\right)\left(x+y\right)\left(x-z\right)+\left(z-x\right)\left(z+x\right)\left(x-y\right)\)
\(=\left(x-y\right).\left[\left(x+y\right)\left(x-z\right)+\left(z-x\right).\left(x+z\right)\right]\)
\(=\left(x-y\right)\left(x^2-zx+xy-yz+zx+z^2-x^2-xz\right)\)
\(=\left(x-y\right)\left(z^2-zx+xy-yz\right)\)
\(=\left(x-y\right)\left[z.\left(z-x\right)-y.\left(z-x\right)\right]\)
\(=\left(x-y\right)\left(z-y\right)\left(z-x\right)\)
\(=\left(x-y\right)\left(y-z\right)\left(x-z\right)\)