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

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

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factor x^7-a^7b^7

factor

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

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

Solution steps

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

Rewrite

a^{7} b^{7}

(ab)^{7}

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

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

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

Simplify

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

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

\frac{( 2 + h ) ^{2} - 4}{h}

x^{6} - 3 x^{4} + 3 x^{2} - 1

e^{a t} u (- t)

2 cos^{2} (x) - 3 cos (x) + 1

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

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