Simplify.
-$$\frac { ( 6 x + h ) ^ { 3 } - 216 x ^ { 3 } } { h }$$
A)
$\frac { 108 x ^ { 3 } + 108 x ^ { 2 } h + 18 x h ^ { 2 } + h ^ { 3 } } { h }$
B) $108 x ^ { 2 } + 18 x h + h ^ { 2 }$
C) $108 x ^ { 2 } h + 18 x h ^ { 2 } + h ^ { 3 }$
D) $36 x ^ { 2 } + 12 x h + h ^ { 2 }$

Question

Quizplus · Accepted Answer

To simplify the given expression, we can expand $(6x + h)^3$ using the binomial theorem and then subtract $216x^3$. The binomial expansion of $(6x + h)^3$ is $216x^3 + 108x^2h + 18xh^2 + h^3$. Subtracting $216x^3$ from this gives $108x^2h + 18xh^2 + h^3$. When we divide this by $h$, we get $108x^2 + 18xh + h^2$, which matches option B.

Simplify - (6x+h)3−216x3h\frac { ( 6 x + h ) ^ { 3 } - 216 x ^ { 3 } } { h }h(6x+h)3−216x3​

Simplify
- $\frac { ( 6 x + h ) ^ { 3 } - 216 x ^ { 3 } } { h }$