Find the first three terms of the expansion. $$\left( p + q ^ { 2 } \right) ^ { 12 }$$
A) $p ^ { 12 } + 12 p ^ { 11 } q + 66 p ^ { 10 } q ^ { 2 }$
B) $p ^ { 12 } + 12 p ^ { 11 } q ^ { 2 } + 24 p ^ { 10 } q ^ { 4 }$
C) $p ^ { 12 } + 12 p ^ { 11 } q + 24 p ^ { 10 } q ^ { 2 }$
D) $p ^ { 12 } + 12 p ^ { 11 } q ^ { 2 } + 66 p ^ { 10 } q ^ { 4 }$

Question

Quizplus · Accepted Answer

The binomial expansion of $(p + q^2)^{12}$ gives terms of the form $\binom{12}{k} p^{12-k} (q^2)^k$. The first three terms are for $k=0, 1, 2$, which are $p^{12}$, $12p^{11}q^2$, and $66p^{10}q^4$.

Find the First Three Terms of the Expansion (p+q2)12\left( p + q ^ { 2 } \right) ^ { 12 }(p+q2)12

Find the First Three Terms of the Expansion $\left( p + q ^ { 2 } \right) ^ { 12 }$