1) \(\left(x+2\right)\left(x+3\right)\left(x+4\right)\left(x+5\right)-24\)
\(=\left[\left(x+2\right)\left(x+5\right)\right]\left[\left(x+3\right)\left(x+4\right)\right]-24\)
\(=\left(x^2+7x+10\right)\left(x^2+7x+12\right)-24\)
Đặt \(x^2+7x+11=a\), ta có:
\(=\left(a+1\right)\left(a-1\right)-24\)
\(=a^2-1-24\)
\(=a^2-25\)
\(=\left(a-5\right)\left(a+5\right)\)
\(=\left(x^2+7x+11-5\right)\left(x^2+7x+11+5\right)\)
\(=\left(x^2+7x+6\right)\left(x^2+7x+16\right)\)
\(=\left(x^2+6x+x+6\right)\left(x^2+7x+16\right)\)
\(=\left[x\left(x+6\right)+\left(x+6\right)\right]\left(x^2+7x+16\right)\)
\(=\left(x+6\right)\left(x+1\right)\left(x^2+7x+16\right)\)
2) \(\left(x^2+x\right)^2+4\left(x^2+x\right)-12\)
\(=\left(x^2+x\right)^2+2\left(x^2+x\right).2+4-4-12\)
\(=\left(x^2+x+2\right)^2-16\)
\(=\left(x^2+x+2\right)^2-4^2\)
\(=\left(x^2+x+2-4\right)\left(x^2+x+2+4\right)\)
\(=\left(x^2+x-2\right)\left(x^2+x+6\right)\)
3) \(\left(x^2+x+1\right)\left(x^2+x+2\right)-12\)
Đặt \(x^2+x+1=a\), ta được
\(=a\left(a+1\right)-12\)
\(=a^2+a-12\)
\(=a^2+2.a.\dfrac{1}{2}+\dfrac{1}{4}-\dfrac{1}{4}-12\)
\(=\left(a+\dfrac{1}{2}\right)^2-\dfrac{49}{4}\)
\(=\left(a+\dfrac{1}{2}\right)^2-\left(\dfrac{7}{2}\right)^2\)
\(=\left(a+\dfrac{1}{2}-\dfrac{7}{2}\right)\left(a+\dfrac{1}{2}+\dfrac{7}{2}\right)\)
\(=\left(a-3\right)\left(a+4\right)\)
\(=\left(x^2+x+1-3\right)\left(x^2+x+1+4\right)\)
\(=\left(x^2+x-2\right)\left(x^2+x+5\right)\)
4) \(\left(a^2-4\right)\left(a^2+6a+5\right)\)
\(=\left(a-2\right)\left(a+2\right)\left(a^2+5a+a+5\right)\)
\(=\left(a-2\right)\left(a+2\right)\left[a\left(a+5\right)+\left(a+5\right)\right]\)
\(=\left(a-2\right)\left(a+2\right)\left(a+5\right)\left(a+1\right)\)
nhờ mn là giúp mình với ạ , minh đang cần gấp :( 
