Question

Phân tích thành nhân tử : (x – 1)(x + 1)(x + 3)(x + 5) + 7

Answer 1

\(=\left[\left(x-1\right)\left(x+5\right)\right]\left[\left(x+1\right)\left(x+3\right)\right]+7\\ =\left(x^2+4x-5\right)\left(x^2+4x+3\right)+7\\ =\left(x^2+4x-1-4\right)\left(x^2+4x-1+4\right)+7\\ =\left(x^2+4x-1\right)^2-16+7\\ =\left(x^2+4x-1\right)^2-9=\left(x^2+4x-4\right)\left(x^2+4x+2\right)\)

Answer 2

\(\left(x-1\right)\left(x+1\right)\left(x+3\right)\left(x+5\right)+7\)

\(=\left(x^2+4x-5\right)\left(x^2+4x+3\right)+7\)

\(=\left(x^2+4x\right)^2-2\left(x^2+4x\right)-8\)

\(=\left(x^2+4x-4\right)\left(x^2+4x+2\right)\)