What is ((x^8-1))/((x-1)) ?

The solution to ((x^8-1))/((x-1)) is (x^4+1)(x^2+1)(x+1)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ((x^8-1))/((x-1))

simplify

\frac{( x ^{8} - 1 )}{( x - 1 )}

(x^{4} + 1) (x^{2} + 1) (x + 1)

Solution steps

\frac{x ^{8} - 1}{x - 1}

Apply exponent rules

= \frac{( x ^{4} ) ^{2} - 1 ^{2}}{x - 1}

Apply Difference of Two Squares Formula:

x^{2} - y^{2} = (x + y) (x - y)

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

= \frac{( x ^{4} + 1 ) ( x ^{4} - 1 )}{x - 1}

Apply exponent rules

= \frac{( x ^{4} + 1 ) ( ( x ^{2} ) ^{2} - 1 ^{2} )}{x - 1}

Apply Difference of Two Squares Formula:

x^{2} - y^{2} = (x + y) (x - y)

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

= \frac{( x ^{4} + 1 ) ( x ^{2} + 1 ) ( x ^{2} - 1 )}{x - 1}

Factor

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

= \frac{( x ^{4} + 1 ) ( x ^{2} + 1 ) ( x + 1 ) ( x - 1 )}{x - 1}

Cancel the common factor:

x - 1

= (x^{4} + 1) (x^{2} + 1) (x + 1)

3 (x + 1) (x - 2)

lo g_{10} (a^{3}) (b)

64 x^{2} - 625 y^{2}

2 \cdot [(a - b) + 1]

\frac{( y - 8 )}{8} \cdot \frac{( 12 x )}{( y - 5 )}

What is ((x^8-1))/((x-1)) ?
The solution to ((x^8-1))/((x-1)) is (x^4+1)(x^2+1)(x+1)