What is factor 8x^9+27y^{15} ?

The solution to factor 8x^9+27y^{15} is (2x^3+3y^5)(4x^6-6x^3y^5+9y^{10})

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factor 8x^9+27y^{15}

factor

8 x^{9} + 27 y^{15}

(2 x^{3} + 3 y^{5}) (4 x^{6} - 6 x^{3} y^{5} + 9 y^{10})

Solution steps

8 x^{9} + 27 y^{15}

Apply exponent rules

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

Apply Sum of Cubes Formula:

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

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

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

Simplify

(2 x^{3})^{2} - 2 x^{3} \cdot 3 y^{5} + (3 y^{5})^{2} : 4 x^{6} - 6 x^{3} y^{5} + 9 y^{10}

= (2 x^{3} + 3 y^{5}) (4 x^{6} - 6 x^{3} y^{5} + 9 y^{10})

x^{2} + 4 x = 140

x = x^{2} - 6 x + 5

198

\frac{2}{3} x - \frac{3}{4} + \frac{1}{4} x = x - \frac{5}{4}

3 n^{2} + 4 n + 1

What is factor 8x^9+27y^{15} ?
The solution to factor 8x^9+27y^{15} is (2x^3+3y^5)(4x^6-6x^3y^5+9y^{10})