a) \(\left(2x-1\right)^2-2\left(2x-1\right)-3\)
\(=\left(2x-1\right)^2+\left(2x-1\right)-3\left(2x-1\right)-3\)
\(=\left(2x-1\right).2x-3.2x\)
\(=2x\left(2x-4\right)=4x\left(x-2\right)\)
b)\(\left(a-b\right)^3+\left(b-c\right)^3+\left(c-a\right)^3\)
\(=\left(a-b+b-c\right)\left[\left(a-b\right)^2-\left(a-b\right)\left(b-c\right)+\left(b-c\right)^2\right]+\left(c-a\right)^3\)
\(=\left(a-c\right)\left[\left(a-b\right)^2-\left(a-b\right)\left(b-c\right)+\left(b-c\right)^2\right]-\left(a-c\right)^3\)
\(=\left(a-c\right)\left[\left(a-b\right)^2-\left(a-b\right)\left(b-c\right)+\left(b-c\right)^2-\left(a-c\right)^2\right]\)
\(=\left(a-c\right)\left[\left(a-b\right)^2-\left(a-b\right)\left(b-c\right)+\left(b-c-a+c\right)\left(b-c+a-c\right)\right]\)
\(=\left(a-c\right)\left[\left(a-b\right)^2-\left(a-b\right)\left(b-c\right)-\left(a-b\right)\left(a+b-2c\right)\right]\)
\(=\left(a-c\right)\left(a-b\right)\left(a-b-b+c-a-b+2c\right)\)
\(=\left(a-c\right)\left(a-b\right)\left(3c-3b\right)\)
\(=3\left(a-c\right)\left(a-b\right)\left(c-b\right)\)
c)\(x\left(x+3\right)\left(x+1\right)\left(x+2\right)-8\)
\(=\left(x^2+3x\right)\left(x^2+3x+2\right)-8\)
\(=\left(x^2+3x\right)^2+2\left(x^2+3x\right)-8\)
\(=\left(x^2+3x\right)^2+4\left(x^2+3x\right)-2\left(x^2+3x\right)-8\)
\(=\left(x^2+3x\right)\left(x^2+3x+4\right)-2\left(x^2+3x+4\right)\)
\(=\left(x^2+3x-2\right)\left(x^2+3x+4\right)\)
\(=\left(x^2+2.\dfrac{3}{2}x+\left(\dfrac{3}{2}\right)^2-\dfrac{17}{4}\right)\left(x^2+3x+4\right)\)
\(=\left[\left(x+\dfrac{3}{2}\right)^2-\left(\dfrac{\sqrt{17}}{2}\right)^2\right]\left(x^2+3x+4\right)\)
\(=\left(x+\dfrac{3}{2}-\dfrac{\sqrt{17}}{2}\right)\left(x+\dfrac{3}{2}+\dfrac{\sqrt{17}}{2}\right)\left(x^2+3x+4\right)\)
nhờ mn là giúp mình với ạ , minh đang cần gấp :( 
