a) \(\left(x^2+x\right)^2-2.\left(x^2+x\right)-15\)
\(=\left(x^2+x\right)^2-2.\left(x^2+x\right)+1-16\)
\(=\left(x^2+x-1\right)^2-16\)
\(=\left(x^2+x-1\right)^2-4^2\)
\(=\left(x^2+x-1-4\right).\left(x^2+x-1+4\right)\)
\(=\left(x^2+x-5\right).\left(x^2+x+3\right)\)
b) \(x^2+2xy+y^2-x-y-12\)
\(=\left(x+y\right)^2-\left(x+y\right)-12\)
\(=\left[\left(x+y\right)^2-4.\left(x+y\right)\right]+\left[3.\left(x+y\right)-12\right]\)
\(=\left(x+y\right).\left(x+y-4\right)+3.\left(x+y-4\right)\)
\(=\left(x+y-4\right).\left(x+y+3\right)\)
Chúc bạn học tốt!
