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 Sum 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)

2 a - {7 a - (3 a - 7 b) + (10 a - 9 b)}

27 r^{3} - 8

\frac{y ^{2} + 2 y - 3}{y ^{2} - 3 y - 18} \cdot \frac{4 y ^{2} - 24 y}{2 y ^{2} - 2 y}

\frac{29}{6}

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