Find the $6$ th term in the expansion of $( 2 x + y ) ^ { 8 }$ .
A) $28 x ^ { 3 } y ^ { 6 }$
B) $224 x ^ { 2 } y ^ { 6 }$
C) $28 x ^ { 2 } y ^ { 6 }$
D) $448 x ^ { 3 } y ^ { 5 }$
E) $112 x ^ { 3 } y ^ { 5 }$

Question

Quizplus · Accepted Answer

The $6$th term in the expansion of $(2x + y)^8$ can be found using the binomial theorem formula for the $n$th term: $T_{n+1} = \binom{n}{r}a^{n-r}b^r$, where $n$ is the power of the binomial, $r$ is the term number minus 1, $a$ and $b$ are the terms of the binomial. For the $6$th term, $r = 5$, so we calculate $T_6 = \binom{8}{5}(2x)^{8-5}y^5 = 56 \cdot 8x^3y^5 = 448x^3y^5$.

Find The 666 Th Term in the Expansion Of (2x+y)8( 2 x + y ) ^ { 8 }(2x+y)8

Find The $6$ Th Term in the Expansion Of $( 2 x + y ) ^ { 8 }$