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

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

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factor 8a^3b^3-27

factor

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

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

Solution steps

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

Apply exponent rules

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

Apply Difference of Cubes Formula:

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

(2 ab)^{3} - 3^{3} = (2 ab - 3) ((2 ab)^{2} + 3 \cdot 2 ab + 3^{2})

= (2 ab - 3) ((2 ab)^{2} + 3 \cdot 2 ab + 3^{2})

Simplify

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

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

6 a + 3 (a - 2)

a^{2} + 2 3 a - 24

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

x \cdot 2 - 6 \frac{x}{5} + \frac{4}{25}

lo g_{10} \frac{( 1 + cos ( \frac{( 5 x )}{2} ) )}{( 1 - cos ( \frac{( 5 x )}{2} ) )}

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