\(a,14x^2y-21xy^2+28x^2y^2=7xy\left(x-3y+4xy\right)\\ b,x\left(x+y\right)-5x-5y=x\left(x+y\right)-5\left(x+y\right)=\left(x+y\right)\left(x-5\right)\\ c,10x\left(x-y\right)-8\left(y-x\right)=10x\left(x-y\right)+8\left(x-y\right)=\left(x-y\right)\left(10x+8\right)=2\left(x-y\right)\left(5x+4\right)\)

\(d,\left(3x+1\right)^2-\left(x+1\right)^2=\left(3x+1-x-1\right)\left(3x+1+x+1\right)=2x\left(4x+2\right)=4x\left(2x+1\right)\)\(e,x^3+y^3+z^3-3xyz=\left(x+y+z\right)\left(x^2+y^2+z^2-xy-yz-zx\right)+3xyz-3xyz=\left(x+y+z\right)\left(x^2+y^2+z^2-xy-yz-zx\right)\)

c: \(=\left(5x-y\right)\left(5x+y\right)\)

e: \(=\left(x-2\right)\left(x-3\right)\)

a) x(4y-10x)

b)3(x+2y)+(x+1)

c)(5x-y)(5x+y)

d)5x(y-z)²

e)(x-3)(x-2)

f)(2x+y)³

ngất

a)

(x+y)^2-9x^2 = (x+y-9x)(x+y+9x)=(y-8x)(10x+y)

b,x^2+4-y^2+4x=(x²-y²)+(4+4x)=(x-y)(x+y)+4(1+x)

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)

\(x^3+y^3+z^3-3xyz=(x+y)^3-3xy(x+y)+z^3-3xyz\)

\(=[(x+y)^3+z^3]-3xy(x+y+z)\)

\(=(x+y+z)[(x+y)^2-z(x+y)+z^2]-3xy(x+y+z)\)

\(=(x+y+z)[(x+y)^2-z(x+y)+z^2-3xy]\)

\(=(x+y+z)(x^2+y^2+z^2-xy-yz-xz)\)

a) \(14x^2y-21xy^2+28x^2y^2=7xy\left(2x-3y+4xy\right)\)

b) \(3x^2-3xy-5x+5y=3x\left(x-y\right)-5\left(x-y\right)=\left(3x+5\right)\left(x-y\right)\)

a: \(x^4+2x^3+x^2=x^2\left(x+1\right)^2\)

b: \(5x^2+5xy-x-y\)

\(=5x\left(x+y\right)-\left(x+y\right)\)

\(=\left(x+y\right)\left(5x-1\right)\)