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

The solution to factor a^3b^6+27c^6d^3 is (ab^2+3c^2d)(a^2b^4-3ab^2c^2d+9c^4d^2)

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factor a^3b^6+27c^6d^3

factor

a^{3} b^{6} + 27 c^{6} d^{3}

(a b^{2} + 3 c^{2} d) (a^{2} b^{4} - 3 a b^{2} c^{2} d + 9 c^{4} d^{2})

Solution steps

a^{3} b^{6} + 27 c^{6} d^{3}

Rewrite

a^{3} b^{6}

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

Rewrite

27 c^{6} d^{3}

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

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

Apply Sum of Cubes Formula:

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

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

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

Simplify

(a b^{2} + 3 c^{2} d) ((a b^{2})^{2} - 3 c^{2} d a b^{2} + (3 c^{2} d)^{2}) : (a b^{2} + 3 c^{2} d) (a^{2} b^{4} - 3 a b^{2} c^{2} d + 9 c^{4} d^{2})

= (a b^{2} + 3 c^{2} d) (a^{2} b^{4} - 3 a b^{2} c^{2} d + 9 c^{4} d^{2})

x^{5} - 3 x

[2.1]

\frac{d}{d y} ((x) (3 x^{2}))

(2 x + 6 x)^{2}

a x + 2 a y - 8 x - 16 y

What is factor a^3b^6+27c^6d^3 ?
The solution to factor a^3b^6+27c^6d^3 is (ab^2+3c^2d)(a^2b^4-3ab^2c^2d+9c^4d^2)