use pascals triangle to complete the expansion of $(q - r)^{5}$.
$q^{5}-5 q^{4} r+10 q^{3} r^{2}+q^{2} r^{3}+5 q r^{4}-r^{5}$

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Accepted Answer

# Explanation:
## Step1: Recall Pascal's Triangle for power 5
Pascal's Triangle row for power $n = 5$ is $1,5,10,10,5,1$.
## Step2: Apply binomial expansion formula $(a + b)^n=\sum_{k = 0}^{n}\binom{n}{k}a^{n - k}b^{k}$. Here $a=q$, $b=-r$, $n = 5$
The expansion is $(q+(-r))^{5}=\binom{5}{0}q^{5}(-r)^{0}+\binom{5}{1}q^{4}(-r)^{1}+\binom{5}{2}q^{3}(-r)^{2}+\binom{5}{3}q^{2}(-r)^{3}+\binom{5}{4}q^{1}(-r)^{4}+\binom{5}{5}q^{0}(-r)^{5}$
$$
\begin{align*}
&=q^{5}- 5q^{4}r + 10q^{3}r^{2}-10q^{2}r^{3}+5qr^{4}-r^{5}
\end{align*}
$$

# Answer:
$-10$

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Question

Explanation:

Step1: Recall Pascal's Triangle for power 5

Step2: Apply binomial expansion formula \((a + b)^n=\sum_{k = 0}^{n}\binom{n}{k}a^{n - k}b^{k}\). Here \(a=q\), \(b=-r\), \(n = 5\)

Answer: