a, \(x^2-8y^2+6x+9\)
\(=\left(x+3\right)^2-8y^2\)
\(=\left(x+3-\sqrt{8}y\right)\left(x+3+\sqrt{8}y\right)\)
b, \(\left(4x+1\right)\left(12x-1\right)\left(3x+2\right)\left(x+1\right)-4\)
\(=\left[\left(4x+1\right)\left(3x+2\right)\right]\left[\left(12x-1\right)\left(x+1\right)\right]-4\)
\(=\left(12x^2+8x+3x+2\right)\left(12x^2+12x-x-1\right)-4\)
\(=\left(12x^2+11x+2\right)\left(12x^2+11x-1\right)-4\)(1)
Đặt \(12x^2+11x+2=a\Rightarrow12x^2+11x-1=a-3\)
\(\Rightarrow\left(1\right)=a\left(a-3\right)-4=a^2-3a-4\)
\(=a^2+a-4a-4=a\left(a+1\right)-4\left(a+1\right)\)
\(=\left(a+1\right)\left(a-4\right)\)(*)
Vì \(a=12x^2+11x+2\) nên:
\(\left(\text{*}\right)=\left(12x^2+11x+3\right)\left(12x^2+11x-2\right)\)
Chúc bạn học tốt!!!