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Use the Binomial Theorem to complete the expansion of $(r + s)^2$ . $\newline$ $r^\square + 2rs + s^2$

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Binomial Theorem II

Full solution

Q. Use the Binomial Theorem to complete the expansion of

(r + s)^2

.

\newline

r^\square + 2rs + s^2

Binomial Theorem Explanation: The Binomial Theorem states that $(a + b)^n = \Sigma_{k=0}^{n} \binom{n}{k} \cdot a^{(n-k)} \cdot b^k$ , where $\Sigma$ denotes the sum over $k$ from $0$ to $n$ . For $(r + s)^2$ , $n = 2$ . We need to find the coefficient when $k = 1$ .
Calculate Coefficient: Calculate the coefficient using ＂ $2$ choose $1$ ＂ which is rac{2!}{1! * (2-1)!} = 2.
Multiply Coefficient: Multiply this coefficient by $r^{2-1} \times s^1$ to get the term with $rs$ . $\newline$ $2 \times r^{2-1} \times s^1 = 2 \times r \times s = 2rs$ .
Complete Expansion: Now we have the complete expansion: $r^2 + 2rs + s^2$ .

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