因式分解x^4+81,x^2+81
问题描述：
因式分解x^4+81,x^2+81
答
x^4+81
=x^4+18x^2+81-18x^2
=(x^2+9)^2-18x^2
=(x^2+9-3√2x)(x^2+9+3√2x)
x^2+81
=x^2+18x+81-18x
=(x+9)^2-18x
=[x+9-3√(2x)][x+9+3√(2x)](x>0)
=[x+9-3i√(-2x)][x+9+3i√(-2x)](x