use pascals triangle to expand $(r + s)^{3}$.

Question

Accepted Answer

# Explanation:
## Step1: Find the row in Pascal's Triangle for exponent 3
The row for exponent $n = 3$ in Pascal's Triangle is $1,3,3,1$.
## Step2: Apply the binomial expansion formula $(a + b)^n=\sum_{k = 0}^{n}\binom{n}{k}a^{n - k}b^{k}$
Here $a=r$, $b = s$, $n = 3$.
$$
\begin{align*}
(r + s)^3&=\binom{3}{0}r^{3}s^{0}+\binom{3}{1}r^{2}s^{1}+\binom{3}{2}r^{1}s^{2}+\binom{3}{3}r^{0}s^{3}\
&=1\times r^{3}\times1+3\times r^{2}\times s+3\times r\times s^{2}+1\times1\times s^{3}
\end{align*}
$$

# Answer:
$r^{3}+3r^{2}s + 3rs^{2}+s^{3}$

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Question

Explanation:

Step1: Find the row in Pascal's Triangle for exponent 3

Step2: Apply the binomial expansion formula \((a + b)^n=\sum_{k = 0}^{n}\binom{n}{k}a^{n - k}b^{k}\)

Answer: