What is factor a^7b^7-x^7 ?

The solution to factor a^7b^7-x^7 is (ab-x)(a^6b^6+a^5b^5x+a^4b^4x^2+a^3b^3x^3+a^2b^2x^4+abx^5+x^6)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

factor a^7b^7-x^7

factor

a^{7} b^{7} - x^{7}

(ab - x) (a^{6} b^{6} + a^{5} b^{5} x + a^{4} b^{4} x^{2} + a^{3} b^{3} x^{3} + a^{2} b^{2} x^{4} + ab x^{5} + x^{6})

Solution steps

a^{7} b^{7} - x^{7}

Rewrite

a^{7} b^{7}

(ab)^{7}

= (ab)^{7} - x^{7}

Apply factoring rule:

x^{n} - y^{n} = (x - y) (x^{n - 1} + x^{n - 2} y + \dots + x y^{n - 2} y^{n - 1})

(ab)^{7} - x^{7} = (ab - x) ((ab)^{6} + x (ab)^{5} + x^{2} (ab)^{4} + x^{3} (ab)^{3} + x^{4} (ab)^{2} + x^{5} ab + x^{6})

= (ab - x) ((ab)^{6} + x (ab)^{5} + x^{2} (ab)^{4} + x^{3} (ab)^{3} + x^{4} (ab)^{2} + x^{5} ab + x^{6})

Simplify

(ab - x) ((ab)^{6} + x (ab)^{5} + x^{2} (ab)^{4} + x^{3} (ab)^{3} + x^{4} (ab)^{2} + x^{5} ab + x^{6}) : (ab - x) (a^{6} b^{6} + a^{5} b^{5} x + a^{4} b^{4} x^{2} + a^{3} b^{3} x^{3} + a^{2} b^{2} x^{4} + ab x^{5} + x^{6})

= (ab - x) (a^{6} b^{6} + a^{5} b^{5} x + a^{4} b^{4} x^{2} + a^{3} b^{3} x^{3} + a^{2} b^{2} x^{4} + ab x^{5} + x^{6})

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

64 y x^{2} - 81 y + 64 z x^{2} - 81 z

1 - 12 x + 3 6^{2}

xx + 2 x + 4

(sin (6 sin (x)))^{2}

What is factor a^7b^7-x^7 ?
The solution to factor a^7b^7-x^7 is (ab-x)(a^6b^6+a^5b^5x+a^4b^4x^2+a^3b^3x^3+a^2b^2x^4+abx^5+x^6)