1: \(4x^2-25+\left(2x+7\right)\left(5-2x\right)\)
=(2x-5)(2x+5)-(2x+7)(2x-5)
=(2x-5)(2x+5-2x-7)
=-2(2x-5)
2: \(3\left(x+4\right)-x^2-4x\)
=3(x+4)-x(x+4)
=(x+4)(3-x)
3: \(5x^2-5y^2-10x+10y\)
\(=5\left(x^2-y^2\right)-10\left(x-y\right)\)
=5(x-y)(x+y)-10(x-y)
=5(x-y)(x+y-2)
4: \(x^2-xy+x-y\)
=x(x-y)+(x-y)
=(x-y)(x+1)
5: \(ax-bx-a^2+2ab-b^2\)
=x(a-b)-(a-b)^2
=(a-b)(x-a+b)
6: \(x^2+4x-y^2+4\)
\(=\left(x^2+4x+4\right)-y^2\)
\(=\left(x+2\right)^2-y^2=\left(x+2+y\right)\left(x+2-y\right)\)
7: \(x^3-x^2-x+1\)
\(=x^2\left(x-1\right)-\left(x-1\right)\)
\(=\left(x-1\right)\left(x^2-1\right)=\left(x-1\right)^2\cdot\left(x+1\right)\)
8: \(x^4+6x^2y+9y^2-1\)
\(=\left(x^2+3y\right)^2-1\)
\(=\left(x^2+3y-1\right)\left(x^2+3y+1\right)\)
9: \(x^3+x^2y-4x-4y\)
\(=x^2\left(x+y\right)-4\left(x+y\right)\)
\(=\left(x+y\right)\left(x^2-4\right)=\left(x+y\right)\left(x+2\right)\left(x-2\right)\)
10: \(x^3-3x^2+1-3x\)
\(=\left(x^3+1\right)-3x\left(x+1\right)\)
\(=\left(x+1\right)\left(x^2-x+1\right)-3x\left(x+1\right)=\left(x+1\right)\left(x^2-4x+1\right)\)
11: \(3x^2-6xy+3y^2-12z^2\)
\(=3\left(x^2-2xy+y^2-4z^2\right)\)
\(=3\left\lbrack\left(x-y\right)^2-\left(2z\right)^2\right\rbrack\)
=3(x-y-2z)(x-y+2z)
12: \(x^2-2x-15\)
\(=x^2-5x+3x-15\)
=x(x-5)+3(x-5)
=(x-5)(x+3)
13: \(2x^2+3x-5\)
\(=2x^2+5x-2x-5\)
=x(2x+5)-(2x+5)
=(2x+5)(x-1)
14: \(2x^2-18=2\left(x^2-9\right)=2\left(x-3\right)\left(x+3\right)\)
15: \(x^2-7xy+10y^2\)
\(=x^2-2xy-5xy+10y^2\)
=x(x-2y)-5y(x-2y)
=(x-2y)(x-5y)
