What is factor a^{12}-2a^6+1 ?

The solution to factor a^{12}-2a^6+1 is (a+1)^2(a-1)^2(a^2+1+a)^2(a^2+1-a)^2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

factor a^{12}-2a^6+1

factor

a^{12} - 2 a^{6} + 1

(a + 1)^{2} (a - 1)^{2} (a^{2} + 1 + a)^{2} (a^{2} + 1 - a)^{2}

Solution steps

a^{12} - 2 a^{6} + 1

Let

u = a^{2}

= u^{6} - 2 u^{3} + 1

Factor

u^{6} - 2 u^{3} + 1 : (u - 1) (u^{2} + u + 1) (u - 1) (u^{2} + u + 1)

= (u - 1) (u^{2} + u + 1) (u - 1) (u^{2} + u + 1)

Substitute back

u = a^{2}

= (a^{2} - 1) (a^{4} + a^{2} + 1) (a^{2} - 1) (a^{4} + a^{2} + 1)

Factor

a^{2} - 1 : (a + 1) (a - 1)

= (a + 1) (a - 1) (a^{4} + a^{2} + 1) (a^{2} - 1) (a^{4} + a^{2} + 1)

Factor

a^{4} + a^{2} + 1 : (a^{2} + 1 + a) (a^{2} + 1 - a)

= (a + 1) (a - 1) (a^{2} + 1 + a) (a^{2} + 1 - a) (a^{2} - 1) (a^{4} + a^{2} + 1)

Factor

a^{2} - 1 : (a + 1) (a - 1)

= (a + 1) (a - 1) (a^{2} + 1 + a) (a^{2} + 1 - a) (a + 1) (a - 1) (a^{4} + a^{2} + 1)

Factor

a^{4} + a^{2} + 1 : (a^{2} + 1 + a) (a^{2} + 1 - a)

= (a + 1) (a - 1) (a^{2} + 1 + a) (a^{2} + 1 - a) (a + 1) (a - 1) (a^{2} + 1 + a) (a^{2} + 1 - a)

Simplify

= (a + 1)^{2} (a - 1)^{2} (a^{2} + 1 + a)^{2} (a^{2} + 1 - a)^{2}

\frac{1}{3} + \frac{5}{12}

\frac{3}{2} (- 2)

(\frac{2}{3}) (\frac{9}{5})

2^{- 3} - 3^{- 2}

6 4^{\frac{- 4}{3}}

What is factor a^{12}-2a^6+1 ?
The solution to factor a^{12}-2a^6+1 is (a+1)^2(a-1)^2(a^2+1+a)^2(a^2+1-a)^2