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ukm theo mình thì:
2a^2 + 4ab + 2b^2
= 2 (a^2 + 2ab + b^2)
= 2 (a + b )^2
1, \(xy^3-x^3y=xy\left(y^2-x^2\right)=xy\left(y-x\right)\left(x+y\right)\)
2, \(5x\left(3y+4x-6\right)\)
3, \(3x\left(2-y\right)\)
4, \(x\left(x^2+2x+1\right)=x\left(x+1\right)^2\)
5, \(x\left(4x^2-12x+9\right)=x\left(2x-3\right)^2\)
6, \(2xy\left(x+2y-5x^2y\right)\)
7, \(x^2\left(x^2+2x+1\right)=x^2\left(x+1\right)^2\)
11, \(\left(x+y\right)\left(x-1\right)\)
\(1,xy^3-x^3y=xy\left(y^2-x^2\right)=xy\left(y-x\right)\left(y+x\right)\\ 2,15xy+20x^2-30x=5x\left(3y+4x-6\right)\\ 3,6x-3xy=3x\left(2-y\right)\\ 4,x^3+2x^2+x=x\left(x^2+2x+1\right)=x\left(x+1\right)^2\\ 5,4x^3-12x^2+9x=x\left(4x^2-12x+9\right)=x\left(2x-3\right)^2\\ 6,2x^2y+4xy^2-10x^3y^2=2xy\left(x+2y-5x^2y\right)\\ 11,x\left(x-1\right)-y\left(1-x\right)=x\left(x-1\right)+y\left(x-1\right)=\left(x-1\right)\left(x+y\right)\)
e: Ta có: \(y+2+xy+2x\)
\(=\left(y+2\right)\left(1+x\right)\)
f: \(y-3+xy-3x=\left(y-3\right)\left(x+1\right)\)
g: \(x+y-1-xy=\left(1-y\right)\left(x-1\right)\)
h: \(x^2-4x+4-y^2=\left(x-2-y\right)\left(x-2+y\right)\)
a) x3-2x2-x+2
=x(x2-1)+2(-x2+1)
=x(x2-1)-2(x2-1)
=(x2-1)(x-2)
b)
x2+6x-y2+9
=x2+6x+9-y2
=(x+3)2-y2
=(x+3-y)(x+3+y)
c: \(x^4+x^3-4x^2+x+1\)
\(=x^4-x^3+2x^3-2x^2-2x^2+2x-x+1\)
\(=\left(x-1\right)\left(x^3+2x^2-2x-1\right)\)
\(=\left(x-1\right)\left[\left(x-1\right)\left(x^2+x+1\right)+2x\left(x-1\right)\right]\)
\(=\left(x-1\right)^2\cdot\left(x^2+3x+1\right)\)
ta co: x^3 + 5x -6=x^3-x+6x-6=x.(x^2 - 1) + 6.(x-1) = x.(x-1).(x+1) + 6.(x-1) =(x-1).(x^2+x+6)
4452424574574
\(4x^3+38x^2y+72xy^2-90y^3=2\left(2x^3+19x^2y+36xy^2-45y^3\right)\)
\(=2\left(2x^3+10x^2y+9x^2y+45xy^2-9xy^2-45y^3\right)\)
\(=2\left[2x^2\left(x+5y\right)+9xy\left(x+5y\right)-9y^2\left(x+5y\right)\right]\)
\(=2\left(x+5y\right)\left(2x^2+9xy-9y^2\right)\)