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