Use the Binomial Theorem to expand and simplify the expression. $( r + 2 ) ^ { 5 }$
A) $r ^ { 5 } + 10 r ^ { 4 } + 8 r ^ { 3 } + 80 r ^ { 2 } + 80 r + 32$
B) $r ^ { 5 } + 10 r ^ { 4 } + 36 r ^ { 3 } + 80 r ^ { 2 } + 80 r + 32$
C) $r ^ { 5 } + 10 r ^ { 4 } + 40 r ^ { 3 } + 80 r ^ { 2 } + 80 r + 32$
D) $r ^ { 5 } + 10 r ^ { 4 } + 40 r ^ { 3 } + 80 r ^ { 2 } + 72 r + 36$
E) $r ^ { 5 } + 10 r ^ { 4 } + 40 r ^ { 3 } + 80 r ^ { 2 } + 60 r + 120$

Question

Quizplus · Accepted Answer

The Binomial Theorem states that $(a + b)^n = \sum_{k=0}^{n} \binom{n}{k} a^{n-k} b^k$. For $(r + 2)^5$, the expansion is $r^5 + 5 \cdot 2 \cdot r^4 + 10 \cdot 4 \cdot r^3 + 10 \cdot 8 \cdot r^2 + 5 \cdot 16 \cdot r + 32$, which simplifies to $r^5 + 10r^4 + 40r^3 + 80r^2 + 80r + 32$.

Use the Binomial Theorem to Expand and Simplify the Expression (r+2)5( r + 2 ) ^ { 5 }(r+2)5

Use the Binomial Theorem to Expand and Simplify the Expression $( r + 2 ) ^ { 5 }$