1/ \(3x^2+6x+3-3y^2=3x^2+3x+3x+3-3y^2\)

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

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

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

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

2/ \(25-x^2-y^2+2xy=5^2-\left(x^2+y^2-2xy\right)\)

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

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

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

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

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

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

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

b.10x(x-y)-6y(y-x)=10x(x-y)+6y(x-y)=(10x+6y)(x-y)

c.3x²+5y-3xy-5x=(3x²--3xy)-(5x-5y)=3x(x-y)-5(x-y)=(3x-5)(x-y)

\(7x^3-5x^2=x^2\left(7x-5\right)\)

\(x^2-10x+25=\left(x-5\right)^2\)

\(6x^2-2xy^2+3x-y\) sai đề

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

7x³-5x²=x².(7x-5)

x²-10x+25=(x-5)²

6x²-2xy²+3x-y=(6x²-2xy²)+(3x-y)=2x(3x-y)+(3x-y)=(3x-y)(2x+1)

4x⁴+1=4x⁴+4x²+1-4x²=(2x²+1)²-4x²=(2x²+2x+1).(2x²-2x+1)

4x² -6x= 2x(2x-3)

b) 3x³ -6x²y -24xy + 12x² = \(3x\left(x^2-2xy-8y+4x\right)\)

^c) x² -25 + y² + 2xy\(=x^2+2xy+y^2-25\)\(=\left(x+y\right)^2-5^2\)

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

b, x² + 9x - 10 

= x² + 10x - x -10

= ( x² - x ) +(10x - 10)

=x( x - 1)  + 10 ( x - 1)

= ( x - 1)(x + 10 )

\(a.=-4\left(x^2-2x+1\right)\)

\(=-4\left(x-1\right)^2\)

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

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

 2xy - x² - y² + 36=-(x²-2xy+y²-36)=-(x-y)²-36=-(x-y-6)(x-y+6)