a ) \(\left(x^2+x+1\right)\left(x^2+x+2\right)-12\)
\(=\left(x^2+x+\dfrac{3}{2}-\dfrac{1}{2}\right)\left(x^2+x+\dfrac{3}{2}+\dfrac{1}{2}\right)-12\)
\(=\left(x^2+x+\dfrac{3}{2}\right)^2-\dfrac{1}{4}-12\)
\(=\left(x^2+x+\dfrac{3}{2}\right)^2-\dfrac{49}{4}\)
\(=\left(x^2+x+\dfrac{3}{2}-\dfrac{7}{2}\right)\left(x^2+x+\dfrac{3}{2}+\dfrac{7}{2}\right)\)
\(=\left(x^2+x-2\right)\left(x^2+x+5\right)\)
\(=\left[x\left(x+2\right)-\left(x+2\right)\right]\left(x^2+x+5\right)\)
\(=\left(x-1\right)\left(x+2\right)\left(x^2+x+5\right)\)
b ) \(\left(x+2\right)\left(x+3\right)\left(x+4\right)\left(x+5\right)-24\)
\(=\left[\left(x+2\right)\left(x+5\right)\right]\left[\left(x+3\right)\left(x+4\right)\right]-24\)
\(=\left(x^2+7x+10\right)\left(x^2+7x+12\right)-24\)
\(=\left(x^2+7x+11-1\right)\left(x^2+7x+11+1\right)-24\)
\(=\left(x^2+7x+11\right)^2-1-24\)
\(=\left(x^2+7x+11\right)^2-25\)
\(=\left(x^2+7x+11-5\right)\left(x^2+7x+11+5\right)\)
\(=\left(x^2+7x+6\right)\left(x^2+7x+16\right)\)
\(=\left[x\left(x+1\right)+6\left(x+1\right)\right]\left(x^2+7x+16\right)\)
\(=\left(x+6\right)\left(x+1\right)\left(x^2+7x+16\right)\)
a ) Đặt \(t=x^2+x+1\)
b ) \(\Leftrightarrow\left(x^2+7x+10\right)\left(x^2+7x+12\right)\)
Đặt \(t=x^2+7x+10\)
