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

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

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

factor

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

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

Solution steps

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

Rewrite

8 a^{3} b^{3}

(2 ab)^{3}

Rewrite

27 c^{3}

(3 c)^{3}

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

Apply Difference of Cubes Formula:

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

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

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

Simplify

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

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

27 x^{3} y^{3} - 8 z^{6}

2 π r^{2} + 2 π r

sin (2 t - 12)

- 2 x^{5} + 6

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

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