分解因式a^4-4a^2+4a-1在实数范围内
问题描述：
分解因式a^4-4a^2+4a-1在实数范围内
答
= (a-1)(a^3 + a^2 - 3a + 1)
= (a-1)(a-1)(a^2 + 2a - 1)
= (a-1)^2 * ((a+1)^2 - 2)
= (a-1)^2 * (a+1-2^(1/2))(a+1+2^(1/2))
答
a^4-4a^2+4a-1
a^4-(4a^2-4a+1)
=(a^2)^2-(2a-1)^2
=[a^2+(2a-1)][a^2-(2a-1)]
=(a^2+2a-1)(a^2-2a+1)
=(a-1+√2)(a+1-√2)(a^2-2a+1)
答
a^4-4a^2+4a-1
＝(a-1)(a^3+a^2-3a+1)
=(a-1)(a+1)(a^2+2a-1)
=(a-1)(a+1)(a+1+√2)(a+1-√2)