What is factor 8a^3g^3+27b^3d^6 ?

The solution to factor 8a^3g^3+27b^3d^6 is (2ag+3bd^2)(4a^2g^2-6abd^2g+9b^2d^4)

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factor 8a^3g^3+27b^3d^6

factor

8 a^{3} g^{3} + 27 b^{3} d^{6}

(2 a g + 3 b d^{2}) (4 a^{2} g^{2} - 6 ab d^{2} g + 9 b^{2} d^{4})

Solution steps

8 a^{3} g^{3} + 27 b^{3} d^{6}

Rewrite

8 a^{3} g^{3}

(2 a g)^{3}

Rewrite

27 b^{3} d^{6}

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

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

Apply Sum of Cubes Formula:

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

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

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

Simplify

(2 a g + 3 b d^{2}) ((2 a g)^{2} - 3 b d^{2} \cdot 2 a g + (3 b d^{2})^{2}) : (2 a g + 3 b d^{2}) (4 a^{2} g^{2} - 6 ab d^{2} g + 9 b^{2} d^{4})

= (2 a g + 3 b d^{2}) (4 a^{2} g^{2} - 6 ab d^{2} g + 9 b^{2} d^{4})

(y)^{3}

(3 x) - 1

8 + 2 t^{2} - 4

e^{(x^{2} + y^{2})}

What is factor 8a^3g^3+27b^3d^6 ?
The solution to factor 8a^3g^3+27b^3d^6 is (2ag+3bd^2)(4a^2g^2-6abd^2g+9b^2d^4)