What is factor 27a^3b^3-8c^3d^3 ?

The solution to factor 27a^3b^3-8c^3d^3 is (3ab-2cd)(9a^2b^2+6abcd+4c^2d^2)

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factor 27a^3b^3-8c^3d^3

factor

27 a^{3} b^{3} - 8 c^{3} d^{3}

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

Solution steps

27 a^{3} b^{3} - 8 c^{3} d^{3}

Rewrite

27 a^{3} b^{3}

(3 ab)^{3}

Rewrite

8 c^{3} d^{3}

(2 c d)^{3}

= (3 ab)^{3} - (2 c d)^{3}

Apply Difference of Cubes Formula:

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

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

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

Simplify

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

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

x^{1} 0 - y^{2} 6

2 a x + 3 a + 4 b x + 6 b

A \cdot (B \cdot C)

x^{2} + 21 x + \frac{144}{4}

\frac{( 2 u - 2 )}{( 1 - u )}

What is factor 27a^3b^3-8c^3d^3 ?
The solution to factor 27a^3b^3-8c^3d^3 is (3ab-2cd)(9a^2b^2+6abcd+4c^2d^2)