What is factor 32x^{10}-243y^{15} ?

The solution to factor 32x^{10}-243y^{15} is (2x^2-3y^3)(16x^8+24x^6y^3+36x^4y^6+54x^2y^9+81y^{12})

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factor 32x^{10}-243y^{15}

factor

32 x^{10} - 243 y^{15}

(2 x^{2} - 3 y^{3}) (16 x^{8} + 24 x^{6} y^{3} + 36 x^{4} y^{6} + 54 x^{2} y^{9} + 81 y^{12})

Solution steps

32 x^{10} - 243 y^{15}

Rewrite

32 x^{10}

(2 x^{2})^{5}

Rewrite

243 y^{15}

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

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

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

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

Simplify

(2 x^{2} - 3 y^{3}) ((2 x^{2})^{4} + 3 y^{3} (2 x^{2})^{3} + (3 y^{3})^{2} (2 x^{2})^{2} + (3 y^{3})^{3} \cdot 2 x^{2} + (3 y^{3})^{4}) : (2 x^{2} - 3 y^{3}) (16 x^{8} + 24 x^{6} y^{3} + 36 x^{4} y^{6} + 54 x^{2} y^{9} + 81 y^{12})

= (2 x^{2} - 3 y^{3}) (16 x^{8} + 24 x^{6} y^{3} + 36 x^{4} y^{6} + 54 x^{2} y^{9} + 81 y^{12})

\frac{1}{2} x + 4

d c + 3 c - a d - 3 a

(5 x)^{2} + 4 (5 x) - 12

x - x^{b - 1} + x^{2}

[e^{t} cos (x)]

What is factor 32x^{10}-243y^{15} ?
The solution to factor 32x^{10}-243y^{15} is (2x^2-3y^3)(16x^8+24x^6y^3+36x^4y^6+54x^2y^9+81y^{12})