What is factor a^7+a^6b+a^5b^2+a^4b^3+a^3b^4+a^2b^5+ab^6+b^7 ?

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

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factor a^7+a^6b+a^5b^2+a^4b^3+a^3b^4+a^2b^5+ab^6+b^7

factor

a^{7} + a^{6} b + a^{5} b^{2} + a^{4} b^{3} + a^{3} b^{4} + a^{2} b^{5} + a b^{6} + b^{7}

(a + b) (a^{2} + b^{2}) (a^{4} + b^{4})

Solution steps

a^{7} + a^{6} b + a^{5} b^{2} + a^{4} b^{3} + a^{3} b^{4} + a^{2} b^{5} + a b^{6} + b^{7}

= (a^{7} + a^{6} b + a^{5} b^{2} + a^{4} b^{3}) + (a^{3} b^{4} + a^{2} b^{5} + a b^{6} + b^{7})

Factor out

a^{4}

from

a^{7} + a^{6} b + a^{5} b^{2} + a^{4} b^{3} : a^{4} (a^{3} + a^{2} b + a b^{2} + b^{3})

Factor out

b^{4}

from

a^{3} b^{4} + a^{2} b^{5} + a b^{6} + b^{7} : b^{4} (a^{3} + a^{2} b + a b^{2} + b^{3})

= a^{4} (a^{3} + a^{2} b + a b^{2} + b^{3}) + b^{4} (a^{3} + a^{2} b + a b^{2} + b^{3})

Factor out common term

a^{3} + a^{2} b + a b^{2} + b^{3}

= (a^{3} + a^{2} b + a b^{2} + b^{3}) (a^{4} + b^{4})

Factor

a^{3} + a^{2} b + a b^{2} + b^{3} : (a + b) (a^{2} + b^{2})

= (a + b) (a^{2} + b^{2}) (a^{4} + b^{4})

\frac{2}{2 ^{- 3}}

\frac{5 !}{2 ! \cdot 3 !}

x + 2 = 4 x + 8

x^{2} + 5 x = 14

3 x + 5 = 7

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