a) \(=x\left(x-5\right)+\left(x-5\right)^2=\left(x-5\right)\left(x+x-5\right)=\left(x-5\right)\left(2x-5\right)\)

b) \(=x^2-2.x.10+10^2=\left(x-10\right)^2\)

c) \(=x\left(x+3\right)+2\left(x+3\right)=\left(x+3\right)\left(x+2\right)\)

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

a) 2x³- 3x²
x²( 2 - 3x )

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

a) x² -x = x(x-1)

b) xz+yz-7(x+y)

= z(x+y)-7(x+y)

= (x+y)(z-7)

a) \(3\left(x-y\right)^2+9y\left(y-x\right)^2\)

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

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

\(=3\left(x-y\right)^2\left(3y+1\right)\)

b) \(3\left(x-y\right)^2+9y\left(y-x\right)\)

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

\(=\left(y-x\right)\left[3\left(y-x\right)+9y\right]\)

\(=3\left(y-x\right)\left(y-x+3y\right)\)

\(=3\left(y-x\right)\left(4y-x\right)\)

a: =3(x-y)^2+9y(x-y)^2

=(x-y)^2(3+9y)

=(x-y)^2*3*(y+3)

b: =3(x-y)^2-9y(x-y)

=3(x-y)(x-y-9y)

=3(x-y)(x-10y)

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

b) \(=\left(x^2+2x\right)+\left(10x+20\right)=x\left(x+2\right)+10\left(x+2\right)=\left(x+2\right)\left(x+10\right)\)

c) đặt \(x^2+x+1=t\)

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

a) = (x - 4y)(x + 1)

b) = (x - 3y)^2 - 2^2

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

c) = x^2(x + 3) - 7x(x + 3) + 9(x + 3)

= (x + 3)(x^2 - 7x + 9)

a: \(x^2-4xy+x-4y\)

\(=x\left(x-4y\right)+\left(x-4y\right)\)

\(=\left(x-4y\right)\left(x+1\right)\)

b: \(x^2-6xy+9y^2-4\)

\(=\left(x-3y\right)^2-4\)

\(=\left(x-3y-2\right)\left(x-3y+2\right)\)

\(a,=5x\left(4x-1\right)\\ b,=y^2-\left(x-1\right)^2=\left(y-x+1\right)\left(y+x-1\right)\\ c,=6x^2+3x-4x-2=3x\left(x+2\right)-2\left(x+2\right)=\left(3x-2\right)\left(x+2\right)\)

\(a,x\left(x+6\right)\\ b,\left(9x-1\right)\left(9x+1\right)\\ c,\left(x+y\right)-3^2\\ =\left(x+y-3\right)\left(x+y+3\right)\\ d,\left(x-y\right)\left(x+y\right)-\left(x-y\right)\\ =\left(x-y\right)\left(x+y-1\right)\)

a) \(=x\left(x-19\right)\)

b) \(=\left(x-y-10\right)\left(x-y+10\right)\)

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

d) \(=\left(x+y\right)\left(x+3\right)\)

\(a)x^2-19x\\=x(x-19)\\b)x^2-2xy+y^2-100\\=(x^2-2xy+y^2)-10^2\\=(x-y)^2-10^2\\=(x-y-10)(x-y+10)\\c)xz+yz-5(x+y)\\=(xz+yz)-5(x+y)\\=z(x+y)-5(x+y)\\=(x+y)(z-5)\\d)x^2+3x+xy+3y\\=(3x+3y)+(x^2+xy)\\=3(x+y)+x(x+y)\\=(x+y)(3+x)\)