Factor.
-$0.064 r ^ { 3 } - 0.027 s ^ { 3 }$
A) $( 0.4 r + 0.3 s ) \left( 0.16 r ^ { 2 } - 0.12 r s - 0.09 s ^ { 2 } \right)$
B) $( 0.4 \mathrm { r } - 0.3 \mathrm {~s} ) \left( 0.16 \mathrm { r } ^ { 2 } + 0.12 \mathrm { rs } + 0.09 \mathrm {~s} ^ { 2 } \right)$
C) $( 0.4 \mathrm { r } - \mathrm { s } ) \left( 0.048 \mathrm { r } ^ { 2 } + 0.4 \mathrm { rs } + 0.036 \mathrm {~s} ^ { 2 } \right)$
D) $( 0.4 \mathrm { r } + \mathrm { s } ) \left( 0.048 \mathrm { r } ^ { 2 } - 0.4 \mathrm { rs } - 0.036 \mathrm {~s} ^ { 2 } \right)$

Question

Quizplus · Accepted Answer

The expression $0.064 r ^ { 3 } - 0.027 s ^ { 3 }$ can be factored as a difference of cubes, where $a^3 = 0.064 r^3$ and $b^3 = 0.027 s^3$. The cube root of $0.064$ is $0.4$ and the cube root of $0.027$ is $0.3$, so $a = 0.4r$ and $b = 0.3s$. The difference of cubes formula is $a^3 - b^3 = (a - b)(a^2 + ab + b^2)$, which leads to the correct factorization as option B.

Factor - 0.064r3−0.027s30.064 r ^ { 3 } - 0.027 s ^ { 3 }0.064r3−0.027s3

Factor
- $0.064 r ^ { 3 } - 0.027 s ^ { 3 }$