Dài dòng:
\(x^4+16\)
\(=\left(x^2\right)^2+4^2\)
\(=\left(x^2\right)^2+2x^2.4+4^2-2x^2.4\)
\(=\left(x^2+4\right)^2-8x^2\)
\(=\left(x^2+4\right)^2-\left(2\sqrt{2}x\right)^2\)
\(=\left(x^2+4-2\sqrt{2}x\right)\left(x^2+4+2\sqrt{2}x\right)\)
Ngắn gọn:
\(x^4 + 16\)
\(⇔x^4+8x^2+16-8x^2\)
\(⇔(x^2+4)^2-8x^2\)
\(⇔(x^2+4-2\sqrt2x)(x^2+4+2\sqrt2x)\)