What is factor 512+27a^3 ?

The solution to factor 512+27a^3 is (3a+8)(9a^2-24a+64)

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factor 512+27a^3

factor

512 + 27 a^{3}

(3 a + 8) (9 a^{2} - 24 a + 64)

Solution steps

512 + 27 a^{3}

Write in the standard form

= 27 a^{3} + 512

Apply exponent rules

= (3 a)^{3} + 8^{3}

Apply Sum of Cubes Formula:

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

(3 a)^{3} + 8^{3} = (3 a + 8) (3^{2} a^{2} - 8 \cdot 3 a + 8^{2})

= (3 a + 8) (3^{2} a^{2} - 8 \cdot 3 a + 8^{2})

Simplify

(3 a + 8) (3^{2} a^{2} - 8 \cdot 3 a + 8^{2}) : (3 a + 8) (9 a^{2} - 24 a + 64)

= (3 a + 8) (9 a^{2} - 24 a + 64)

8 x (3 - 2 x)

\frac{1}{\frac{13}{x} - 4}

x^{4} - 13 x^{2} - 12 x

\frac{1}{- 1 + i}

\frac{a ^{10} b ^{20}}{a ^{2} b ^{10}}

What is factor 512+27a^3 ?
The solution to factor 512+27a^3 is (3a+8)(9a^2-24a+64)