What is factor x^{15}+y^{15} ?

The solution to factor x^{15}+y^{15} is (x+y)(x^4-x^3y+x^2y^2-xy^3+y^4)(x^{10}-x^5y^5+y^{10})

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factor x^{15}+y^{15}

factor

x^{15} + y^{15}

(x + y) (x^{4} - x^{3} y + x^{2} y^{2} - x y^{3} + y^{4}) (x^{10} - x^{5} y^{5} + y^{10})

Solution steps

x^{15} + y^{15}

Apply exponent rules

= (x^{5})^{3} + (y^{5})^{3}

Apply Sum of Cubes Formula:

x^{3} + y^{3} = (x + y) (x^{2} - x y + y^{2})

(x^{5})^{3} + (y^{5})^{3} = (x^{5} + y^{5}) ((x^{5})^{2} - x^{5} y^{5} + (y^{5})^{2})

= (x^{5} + y^{5}) ((x^{5})^{2} - x^{5} y^{5} + (y^{5})^{2})

Simplify

(x^{5})^{2} - x^{5} y^{5} + (y^{5})^{2} : x^{10} - x^{5} y^{5} + y^{10}

= (x^{5} + y^{5}) (x^{10} - x^{5} y^{5} + y^{10})

Factor

x^{5} + y^{5} : (x + y) (x^{4} - x^{3} y + x^{2} y^{2} - x y^{3} + y^{4})

= (x + y) (x^{4} - x^{3} y + x^{2} y^{2} - x y^{3} + y^{4}) (x^{10} - x^{5} y^{5} + y^{10})

391000 - 79800 x - x \cdot x

(x + h)^{- 1}

(15 a^{3} b^{4} x^{4}) (3 a^{2} b^{2} x^{3})^{- 1}

4 z^{2} + 23 z - 35

\frac{( 2 x )}{( 3 y - 3 x )} + \frac{( 3 y )}{( 5 x - 5 y )}

What is factor x^{15}+y^{15} ?
The solution to factor x^{15}+y^{15} is (x+y)(x^4-x^3y+x^2y^2-xy^3+y^4)(x^{10}-x^5y^5+y^{10})