1: \(x^2-4xy+3y^2\)
\(=x^2-xy-3xy+3y^2\)
\(=x\left(x-y\right)-3y\left(x-y\right)\)
=(x-y)(x-3y)
2: \(4x^2-5xy+y^2\)
\(=4x^2-4xy-xy+y^2\)
=4x(x-y)-y(x-y)
=(x-y)(4x-y)
4: \(9x^2+6xy-8y^2\)
\(=9x^2+6xy+y^2-9y^2\)
\(=\left(3x+y\right)^2-\left(3y\right)^2\)
\(=\left(3x+y+3y\right)\left(3x+y-3y\right)\)
=(3x+4y)(3x-2y)
5: \(2x^2+3xy-5y^2\)
\(=2x^2-2xy+5xy-5y^2\)
\(=2x\left(x-y\right)+5y\left(x-y\right)\)
=(x-y)(2x+5y)
7: \(x^2-10xy+16y^2\)
\(=x^2-2xy-8xy+16y^2\)
\(=x\left(x-2y\right)-8y\left(x-2y\right)\)
=(x-2y)(x-8y)
8:
\(3x^2-10xy+8y^2\)
\(=3x^2-6xy-4xy+8y^2\)
\(=3x\left(x-2y\right)-4y\left(x-2y\right)\)
=(x-2y)(3x-4y)
10: \(2x^2+10xy+8y^2\)
\(=2\left(x^2+5xy+4y^2\right)\)
\(=2\left(x^2+xy+4xy+4y^2\right)\)
\(=2\left[x\left(x+y\right)+4y\left(x+y\right)\right]\)
\(=2\left(x+y\right)\left(x+4y\right)\)
11: \(5x^2+10xy+5y^2\)
\(=5\left(x^2+2xy+y^2\right)\)
\(=5\left(x+y\right)^2\)