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})

n is odd

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})

5 + 5 e^{5}

(x^{2} sin (4 x)) \cdot 4

(x - 2) + (- x^{'})

n^{2} + n x + n c + c x

10 e - 15

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)