a) \(\left(5x+4\right)^2-49x^2\)
\(=\left(5x+4-7x\right)\left(5x+4+7x\right)\)
\(=\left(4-2x\right)\left(12x+4\right)\)
\(=8\left(2-x\right)\left(3x+1\right)\)
b) \(x^3+2x^2+xy^2\)
\(=x\left(x^2+2x+y^2\right)\)
\(=x\left(x+y\right)^2\)
c)\(x^2-y^2-x+y\)
\(=\left(x-y\right)\left(x+y\right)-\left(x-y\right)\)
\(=\left(x-y\right)\left(x+y-1\right)\)
d) \(4x^2-9y^2+4x-6y\)
\(=\left(2x-3y\right)\left(2x+3y\right)+2\left(2x-3y\right)\)
\(=\left(2x-3y\right)\left(2x+3y+2\right)\)
e) \(-x^2+5x+2xy-5y-y^2\)
\(=-\left(x^2-2xy+y^2\right)+\left(5x-5y\right)\)
\(=-\left(x-y\right)^2+5\left(x-y\right)\)
\(=-\left(x-y\right)\left(x-y-5\right)\)
f) \(y^2\left(x^2+y\right)-zx^2-zy\)
\(=y^2\left(x^2+y\right)-z\left(x^2+y\right)\)
\(=\left(x^2+y\right)\left(y^2-z\right)\)
\(=\left(x^2+y\right)\left(y-\sqrt{z}\right)\left(y+\sqrt{z}\right)\)