Use Pascal's Triangle to complete the expansion of (u + v)^3. u^3 + 3u^2v + ____uv^2 + v^3

Pascal's Triangle Coefficients: Pascal's Triangle for the third row is 1, 3, 3, 1. These are the coefficients for the expansion.Calculate Next Term: The second term is 3u^2v, so the third term will be the next coefficient (3) times u to the power of (3 - 2) times v to the power of 2. So, 3 * u^(3-2) * v^2.Calculate Third Term: Calculate the third term: 3 * u^1 * v^2 = 3uv^2.Complete Expansion: The complete expansion is u^3 + 3u^2v + 3uv^2 + v^3.

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Use Pascal's Triangle to complete the expansion of $(u + v)^3$ . $\newline$ $u^3 + 3u^2v + \underline{\hspace{1cm}}uv^2 + v^3$

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Pascal's triangle and the Binomial Theorem

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Q. Use Pascal's Triangle to complete the expansion of

(u + v)^3

\newline

u^3 + 3u^2v + \underline{\hspace{1cm}}uv^2 + v^3

Pascal's Triangle Coefficients: Pascal's Triangle for the third row is $1, 3, 3, 1$ . These are the coefficients for the expansion.
Calculate Next Term: The second term is $3u^2v$ , so the third term will be the next coefficient $(3)$ times $u$ to the power of $(3 - 2)$ times $v$ to the power of $2$ . So, $3 \times u^{3-2} \times v^2$ .
Calculate Third Term: Calculate the third term: $3 \times u^1 \times v^2 = 3uv^2$ .
Complete Expansion: The complete expansion is $u^3 + 3u^2v + 3uv^2 + v^3$ .