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 Sum 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})

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

D^{2} - 4 D + 2^{2} + 3^{2}

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

10 \cdot \frac{1}{2}

2 (x)^{6} + 7 (x)^{3} + 9

x + y - z + (- 9)

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)