a)
\(14x^2y-21xy^2+28x^2y^2\)
\(=7xy(2x-3y+4xy)\)
b) \(x(x+y)-5x-5y=x(x+y)-5(x+y)=(x-5)(x+y)\)
c)
\(10x(x-y)-8(y-x)=10x(x-y)+8(x-y)\)
\(=(x-y)(10x+8)=2(x-y)(5x+4)\)
a. \(14x^2y-21xy^2+28x^2y^2\)
\(=7xy\left(2x-3y+4xy\right)\)
b. \(x\left(x+y\right)-5x-5y\)
\(=x\left(x+y\right)-5\left(x+y\right)\)
\(=\left(x-5\right)\left(x+y\right)\)
c. \(10x\left(x-y\right)-8\left(y-x\right)\)
\(=10x\left(x-y\right)+8\left(x-y\right)\)
\(=\left(10x+8\right)\left(x-y\right)\)
d. \(\left(3x+1\right)^2-\left(x+1\right)^2\)
\(=\left(3x+1+x+1\right)\left(3x+1-x-1\right)\)
\(=2x\left(4x+2\right)\)
\(=4x\left(2x+1\right)\)
e. Vì bài này giải không ra nên mình nghĩ nó sai đề, sửa lại tí nhé!
\(x^3+y^3+z^3-3xyz\)
\(=\left(x+y\right)^3+z^3-3xy\left(x+y\right)-3xyz\)
\(=\left(x+y+z\right)\left[\left(x+y\right)^2-z\left(x+y\right)+z^2\right]-3xy\left(x+y+z\right)\)
\(=\left(x+y+z\right)\left(x^2+2xy+y^2-xz+zy+z^2-3xy\right)\)
g. \(5x^2-10xy+5y^2-20z^2\)
\(=5\left(x^2-2xy+y^2-4z^2\right)\)
\(=5\left[\left(x-y^2\right)-4z^2\right]\)
\(=5\left(x-y+z\right)\left(x-y-z\right)\)
h. \(x^3-x+3x^2y+3xy^3+y^3-y\)
\(=\left(x^3+3x^2y+3xy^2+y^2\right)-\left(x+y\right)\)
\(=\left(x+y\right)^3-\left(x+y\right)\)
\(=\left(x+y\right)\left[\left(x+y\right)^2-1\right]\)
\(=\left(x+y\right)\left(x+y-1\right)\left(x+y+1\right)\)
i. \(x^2+7x-8\)
\(=x^2-x+8x-8\)
\(=x\left(x-1\right)+8\left(x-1\right)\)
\(=\left(x+8\right)\left(x-1\right)\)
d)
\((3x+1)^2-(x+1)^2=[(3x+1)-(x+1)][(3x+1)+(x+1)]\)
\(=2x(4x+2)=4x(2x+1)\)
e)
\(x^3+y^3+z^3-3xyz=(x+y)^3-3xy(x+y)+z^3-3xyz\)
\(=[(x+y)^3+z^3]-3xy(x+y+z)\)
\(=(x+y+z)[(x+y)^2-z(x+y)+z^2]-3xy(x+y+z)\)
\(=(x+y+z)[(x+y)^2-z(x+y)+z^2-3xy]\)
\(=(x+y+z)(x^2+y^2+z^2-xy-yz-xz)\)
g)
\(5x^2-10xy+5y^2-20z^2\)
\(=5(x^2-2xy+y^2-4z^2)\)
\(=5[(x-y)^2-(2z)^2]=5(x-y-2z)(x-y+2z)\)
h)
\(x^3-x+3x^2y+3xy^3+y^3-y\)
\(=(x^3+y^3)+(3x^2y+3xy^2)-(x+y)\)
\(=(x+y)(x^2-xy+y^2)+3xy(x+y)-(x+y)\)
\(=(x+y)(x^2-xy+y^2+3xy-1)=(x+y)(x^2+2xy+y^2-1)\)
\(=(x+y)[(x+y)^2-1^2]=(x+y)(x+y-1)(x+y+1)\)
i)
\(x^2+7x-8=(x^2-x)+(8x-8)\)
\(=x(x-1)+8(x-1)=(x+8)(x-1)\)
Cho mình hỏi xíu: Mấy bài này có trong sách j z ?