What is factor x^5+32y^5 ?

The solution to factor x^5+32y^5 is (x+2y)(x^4-2x^3y+4x^2y^2-8xy^3+16y^4)

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factor x^5+32y^5

factor

x^{5} + 32 y^{5}

(x + 2 y) (x^{4} - 2 x^{3} y + 4 x^{2} y^{2} - 8 x y^{3} + 16 y^{4})

Solution steps

x^{5} + 32 y^{5}

Apply exponent rules

= x^{5} + (2 y)^{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 i s o dd

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

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

Simplify

(x + 2 y) (x^{4} - 2 x^{3} y + 2^{2} x^{2} y^{2} - 2^{3} x y^{3} + 2^{4} y^{4}) : (x + 2 y) (x^{4} - 2 x^{3} y + 4 x^{2} y^{2} - 8 x y^{3} + 16 y^{4})

= (x + 2 y) (x^{4} - 2 x^{3} y + 4 x^{2} y^{2} - 8 x y^{3} + 16 y^{4})

- \frac{16}{72}

x^{6} - 144 y^{4}

\frac{3}{4} (- 2)

(16 x^{4} y^{5})^{\frac{1}{4}}

(- 7 + 3 x) (4 + 3 x)

What is factor x^5+32y^5 ?
The solution to factor x^5+32y^5 is (x+2y)(x^4-2x^3y+4x^2y^2-8xy^3+16y^4)