What is factor 125a^9b^3-64c^3d^6 ?

The solution to factor 125a^9b^3-64c^3d^6 is (5a^3b-4cd^2)(25a^6b^2+20a^3bcd^2+16c^2d^4)

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factor 125a^9b^3-64c^3d^6

factor

125 a^{9} b^{3} - 64 c^{3} d^{6}

(5 a^{3} b - 4 c d^{2}) (25 a^{6} b^{2} + 20 a^{3} b c d^{2} + 16 c^{2} d^{4})

Solution steps

125 a^{9} b^{3} - 64 c^{3} d^{6}

Rewrite

125 a^{9} b^{3}

(5 a^{3} b)^{3}

Rewrite

64 c^{3} d^{6}

(2^{2} c d^{2})^{3}

= (5 a^{3} b)^{3} - (2^{2} c d^{2})^{3}

Apply Difference of Cubes Formula:

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

(5 a^{3} b)^{3} - (2^{2} c d^{2})^{3} = (5 a^{3} b - 2^{2} c d^{2}) ((5 a^{3} b)^{2} + 2^{2} c d^{2} 5 a^{3} b + (2^{2} c d^{2})^{2})

= (5 a^{3} b - 2^{2} c d^{2}) ((2^{2} c d^{2})^{2} + 2^{2} c d^{2} 5 a^{3} b + (5 a^{3} b)^{2})

Simplify

(5 a^{3} b - 2^{2} c d^{2}) ((5 a^{3} b)^{2} + 2^{2} c d^{2} \cdot 5 a^{3} b + (2^{2} c d^{2})^{2}) : (5 a^{3} b - 4 c d^{2}) (25 a^{6} b^{2} + 20 a^{3} b c d^{2} + 16 c^{2} d^{4})

= (5 a^{3} b - 4 c d^{2}) (25 a^{6} b^{2} + 20 a^{3} b c d^{2} + 16 c^{2} d^{4})

- 15 b^{2 n + 6} x^{2 n + 7}

y (d y)

x e^{- 2 x^{2} - 2 y^{2}}

ab + a y + x b + x y

a y - y + am - m

What is factor 125a^9b^3-64c^3d^6 ?
The solution to factor 125a^9b^3-64c^3d^6 is (5a^3b-4cd^2)(25a^6b^2+20a^3bcd^2+16c^2d^4)