What is factor x^5y^{15}+z^5 ?

The solution to factor x^5y^{15}+z^5 is (xy^3+z)(x^4y^{12}-x^3y^9z+x^2y^6z^2-xy^3z^3+z^4)

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factor x^5y^{15}+z^5

factor

x^{5} y^{15} + z^{5}

(x y^{3} + z) (x^{4} y^{12} - x^{3} y^{9} z + x^{2} y^{6} z^{2} - x y^{3} z^{3} + z^{4})

Solution steps

x^{5} y^{15} + z^{5}

Rewrite

x^{5} y^{15}

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

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

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

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

Simplify

(x y^{3} + z) ((x y^{3})^{4} - (x y^{3})^{3} z + (x y^{3})^{2} z^{2} - x y^{3} z^{3} + z^{4}) : (x y^{3} + z) (x^{4} y^{12} - x^{3} y^{9} z + x^{2} y^{6} z^{2} - x y^{3} z^{3} + z^{4})

= (x y^{3} + z) (x^{4} y^{12} - x^{3} y^{9} z + x^{2} y^{6} z^{2} - x y^{3} z^{3} + z^{4})

(ln (3)) \cdot (7)

0.21 x^{2} + 2.84 - 42.58

y^{(n)}

5 + (- 2)

(2 2^{2})^{2} x

What is factor x^5y^{15}+z^5 ?
The solution to factor x^5y^{15}+z^5 is (xy^3+z)(x^4y^{12}-x^3y^9z+x^2y^6z^2-xy^3z^3+z^4)