Factor.
-$375 \mathrm { k } ^ { 3 } \mathrm {~m} - 192 \mathrm {~m} ^ { 4 }$
A) $3 \mathrm {~m} \left( 5 \mathrm { k } + 4 \mathrm {~m} ^ { 2 } \right) \left( 25 \mathrm { k } ^ { 2 } - 20 \mathrm {~km} + 16 \mathrm {~km} ^ { 2 } \right)$
B) $3 \mathrm {~m} ( 125 \mathrm { k } - 4 \mathrm {~m} ) \left( \mathrm { k } ^ { 2 } + 20 \mathrm {~km} + 16 \mathrm {~m} ^ { 2 } \right)$
C) $\left( 15 k m - 12 m ^ { 2 } \right) \left( 25 k ^ { 2 } + 16 m ^ { 2 } \right)$
D) $3 m ( 5 k - 4 m ) \left( 25 k ^ { 2 } + 20 k m + 16 m ^ { 2 } \right)$

Question

Quizplus · Accepted Answer

The expression $375k^3m - 192m^4$ can be factored by first taking out the greatest common factor, which is $3m$, leaving us with $3m(125k^3 - 64m^3)$. Recognizing $125k^3$ and $64m^3$ as perfect cubes, we can further factor using the difference of cubes formula $a^3 - b^3 = (a - b)(a^2 + ab + b^2)$, where $a = 5k$ and $b = 4m$. This results in $3m(5k - 4m)(25k^2 + 20km + 16m^2)$, matching option D.

Factor - 375k3 m−192 m4375 \mathrm { k } ^ { 3 } \mathrm {~m} - 192 \mathrm {~m} ^ { 4 }375k3 m−192 m4

Factor
- $375 \mathrm { k } ^ { 3 } \mathrm {~m} - 192 \mathrm {~m} ^ { 4 }$