Factor.
-$729 s ^ { 3 } + 1$
A) $( 9 \mathrm {~s} + 1 ) \left( 81 \mathrm {~s} ^ { 2 } - 9 \mathrm {~s} + 1 \right)$
B) $( 9 s + 1 ) \left( 81 s ^ { 2 } + 1 \right)$
C) $( 9 s - 1 ) \left( 81 s ^ { 2 } + 9 s + 1 \right)$
D) $( 729 s + 1 ) \left( s ^ { 2 } - 9 s + 1 \right)$

Question

Quizplus · Accepted Answer

The expression $729s^3 + 1$ is a sum of cubes, which can be factored as $(a^3 + b^3) = (a + b)(a^2 - ab + b^2)$, where $a = 9s$ and $b = 1$. Applying this formula gives $(9s + 1)(81s^2 - 9s + 1)$.

Factor - 729s3+1729 s ^ { 3 } + 1729s3+1 A) (9 s+1)(81 s2−9 s+1)( 9 \mathrm {~s} + 1 ) \left( 81 \mathrm {~s} ^ { 2 } - 9 \mathrm {~s} + 1 \right)(9 s+1)(81 s2−9 s+1)

Factor
- $729 s ^ { 3 } + 1$ A) $( 9 \mathrm {~s} + 1 ) \left( 81 \mathrm {~s} ^ { 2 } - 9 \mathrm {~s} + 1 \right)$