\(x^2y+xy^2+x^2z+xz^2+y^2z+yz^2+3xyz\)

\(=\left(x^2y+xy^2+xyz\right)+\left(y^2z+yz^2+xyz\right)+\left(x^2z+xz^2+xyz\right)\)

\(=xy\left(x+y+z\right)+yz\left(y+z+x\right)+xz\left(x+z+y\right)\)

\(=\left(x+y+z\right)\left(xy+yz+xz\right)\)

a: =5x(x-y)-7(x-y)

=(x-y)(5x-7)

b: =x(x+2y)+(x+2y)

=(x+2y)(x+1)

c; =(x-3)^2-9y^2

=(x-3-3y)(x-3+3y)

a

\(5x^2-5xy+7y-7x\\ =5x\left(x-y\right)+7\left(y-x\right)\\ =5x\left(x-y\right)-7\left(x-y\right)\\ =\left(5x-7\right)\left(x-y\right)\)

b

\(x^2+2xy+x+2y\\ =x\left(x+2y\right)+\left(x+2y\right)\\ =\left(x+1\right)\left(x+2y\right)\)

c

\(x^2-6x-9y^2+9\\ =x^2-6x+9-\left(3y\right)^2\\ =x^2-2.x.3+3^2-\left(3y\right)^2\\ =\left(x-3\right)^2-\left(3y\right)^2\\ =\left(x-3-3y\right)\left(x-3+3y\right)\)

a) 20x²y + 25xy2
= 5xy( 4x + 5y )
b) x² - 5x - 15y - 9y²
= x(x - 5) - 3y(5 + 3y)

Lời giải:

$A=x^2-8xy+15y^2=x^2-3xy-(5xy-15y^2)$

$=x(x-3y)-5y(x-3y)=(x-3y)(x-5y)$

$B=2x^2-5xy+2y^2=(2x^2-4xy)-(xy-2y^2)$

$=2x(x-2y)-y(x-2y)=(2x-y)(x-2y)$

$C=2x^2-3y^2-xy=(2x^2+2xy)-(3y^2+3xy)$

$=2x(x+y)-3y(y+x)=(x+y)(2x-3y)$

a) \(=3\left(5y+4x\right)\)

b) \(=\left(x-3\right)^2\)

c) \(=y\left(y^2+2y+3\right)\)

d) \(=x\left(x+y\right)+6\left(x+y\right)=\left(x+6\right)\left(x+y\right)\)

\(a,=x^2(2x-3)\\ b,=x(x+5y)+(x+5y)=(x+5y)(x+1)\)

a) 2x³- 3x²
x²( 2 - 3x )

b) x²+ 5xy + x + 5y
x ( x + 5y ) + ( x + 5y)
(x + 1 )( x + 5y)