a: \(a^3-3a+3b-b^3\)
\(=\left(a^3-b^3\right)-\left(3a-3b\right)\)
\(=\left(a-b\right)\left(a^2+ab+b^2\right)-3\left(a-b\right)\)
\(=\left(a-b\right)\left(a^2+ab+b^2-3\right)\)
b: \(a^2+6ab+9b^2-1\)
\(=\left(a^2+6ab+9b^2\right)-1\)
\(=\left(a+3b\right)^2-1\)
\(=\left(a+3b-1\right)\left(a+3b+1\right)\)
c: \(4x^2-25+\left(2x+7\right)\left(5-2x\right)\)
\(=\left(4x^2-25\right)-\left(2x+7\right)\left(2x-5\right)\)
\(=\left(2x-5\right)\left(2x+5\right)-\left(2x+7\right)\left(2x-5\right)\)
\(=\left(2x-5\right)\left(2x+5-2x-7\right)\)
\(=-2\cdot\left(2x-5\right)\)
d: \(x^2+2x-15\)
\(=x^2+5x-3x-15\)
\(=\left(x^2+5x\right)-\left(3x+15\right)\)
\(=x\left(x+5\right)-3\left(x+5\right)\)
\(=\left(x+5\right)\left(x-3\right)\)
e: \(2x^3+3x^2-5x\)
\(=x\left(2x^2+3x-5\right)\)
\(=x\left(2x^2+5x-2x-5\right)\)
\(=x\left[x\left(2x+5\right)-\left(2x+5\right)\right]\)
\(=x\left(2x+5\right)\left(x-1\right)\)
f: \(2x^3-4x^2+2x-4\)
\(=2\left(x^3-2x^2+x-2\right)\)
\(=2\left[x^2\left(x-2\right)+\left(x-2\right)\right]\)
\(=2\left(x-2\right)\left(x^2+1\right)\)
g: \(x^3-4x^2-8x+8\)
\(=\left(x^3+8\right)-\left(4x^2+8x\right)\)
\(=\left(x+2\right)\left(x^2-2x+4\right)-4x\left(x+2\right)\)
\(=\left(x+2\right)\left(x^2-2x+4-4x\right)\)
\(=\left(x+2\right)\left(x^2-6x+4\right)\)
h: \(x^2-7xy+10y^2\)
\(=x^2-2xy-5xy+10y^2\)
\(=\left(x^2-2xy\right)-\left(5xy-10y^2\right)\)
\(=x\left(x-2y\right)-5y\left(x-2y\right)\)
\(=\left(x-2y\right)\left(x-5y\right)\)
