Factor the sum of cubes. $125 u ^ { 3 } + 1$
A) $( 5 u - 1 ) \left( 25 u ^ { 2 } + 5 u + 1 \right)$
B) $( 5 u + 1 ) \left( 25 u ^ { 2 } - 5 u + 1 \right)$
C) $( 5 u - 1 ) \left( 25 u ^ { 2 } - 5 u + 1 \right)$
D) $( 5 u + 1 ) \left( 25 u ^ { 2 } + 5 u - 1 \right)$
E) $( 5 u + 1 ) \left( 25 u ^ { 2 } + 5 u + 1 \right)$

Question

Quizplus · Accepted Answer

The sum of cubes can be factored using the formula $a^3 + b^3 = (a + b)(a^2 - ab + b^2)$. Here, $125u^3 = (5u)^3$ and $1 = 1^3$, so $a = 5u$ and $b = 1$. Applying the formula gives $(5u + 1)(25u^2 - 5u + 1)$.

Factor the Sum of Cubes 125u3+1125 u ^ { 3 } + 1125u3+1

Factor the Sum of Cubes $125 u ^ { 3 } + 1$