1: \(2x^2y-6xy^2\)
\(=2xy\cdot x-2xy\cdot3y\)
\(=2xy\left(x-3y\right)\)
2: \(6x^2y^4-15xy^2\)
\(=3xy^2\cdot2xy^2-3xy^2\cdot5\)
\(=3xy^2\left(2xy^2-5\right)\)
3: \(5x^2+10xy+5y^2\)
\(=5\cdot x^2+5\cdot2xy+5\cdot y^2\)
\(=5\left(x^2+2xy+y^2\right)=5\left(x+y\right)^2\)
4: \(9xy-4a^2xy\)
\(=xy\left(9-4a^2\right)\)
\(=xy\left(3-2a\right)\left(3+2a\right)\)
5: \(4x^5y^2-8x^4y^3+4x^3y^4\)
\(=4x^3y^2\cdot x^2-4x^3y^2\cdot2xy+4x^3y^2\cdot y^2\)
\(=4x^3y^2\left(x^2-2xy+y^2\right)\)
\(=4x^3y^2\left(x-y\right)^2\)
6: \(\left(a^2+4\right)^2-16a^2\)
\(=\left(a^2+4+4a\right)\left(a^2+4-4a\right)\)
\(=\left(a+2\right)^2\cdot\left(a-2\right)^2\)
7: \(36a^2-\left(a^2+9\right)^2\)
\(=\left(6a\right)^2-\left(a^2+9\right)^2\)
\(=\left(6a-a^2-9\right)\left(6a+a^2+9\right)\)
\(=-\left(a^2-6a+9\right)\left(a^2+6a+9\right)\)
\(=-\left(a-3\right)^2\cdot\left(a+3\right)^2\)
8: \(x^2+2xy+y^2-25\)
\(=\left(x^2+2xy+y^2\right)-25\)
\(=\left(x+y\right)^2-25=\left(x+y+5\right)\left(x+y-5\right)\)
9: \(y^2-3y+xy-3x\)
\(=\left(y^2-3y\right)+\left(xy-3x\right)\)
\(=y\left(y-3\right)+x\left(y-3\right)\)
\(=\left(y-3\right)\left(x+y\right)\)
10: \(x^2+4x-y^2+4\)
\(=\left(x^2+4x+4\right)-y^2\)
\(=\left(x+2\right)^2-y^2\)
\(=\left(x+2+y\right)\left(x+2-y\right)\)
11: \(x^2-x+5\left(x-1\right)\)
\(=\left(x^2-x\right)+5\left(x-1\right)\)
\(=x\left(x-1\right)+5\left(x-1\right)\)
=(x-1)(x+5)
12: \(x^2-3x+2\)
\(=x^2-x-2x+2\)
\(=x\left(x-1\right)-2\left(x-1\right)\)
=(x-1)(x-2)
