Bài 2:
a) \(\left(x-2\right)\left(x^2+2x+4\right)-6x^2+12\)
\(=x\left(x^2+2x+4\right)-2\left(x^2+2x+4\right)-6x^2+12\\ =x^3+2x^2+4x-2x^2+4x+8-6x^2+12\\ =x^3-6x^2+8x+20\)
b) \(\left(2x+5\right)\left(5-2x\right)+\left(x-5\right)\left(5+4x\right)\)
\(2x\left(5-2x\right)+5\left(5-2x\right)+x\left(5+4x\right)-5\left(5+4x\right)\\ =10x-4x^2+25-10x+5x+4x^2-25-20x\\ =-15x\)
c) \(4x^2+4x+1-\left(2x-1\right)^2\)
\(\left(4x^2+4x+1\right)-\left(2x-1\right)^2\\ =\left(2x+1\right)^2-\left(2x-1\right)^2\\ =\left(2x+1+2x-1\right)\left(2x+1-2x+1\right)\\ =4x.2\\ =8x\)
d) \(\left(x+5\right)\left(x^2+5x+25\right)-10x\left(x+5\right)-x^3\)
\(=x\left(x^2+5x+25\right)+5\left(x^2+5x+25\right)-10x^2-50x-x^3\\ =x^3+5x^2+25x+5x^2+25x+125-10x^2-50x-x^3\\ =125\)
