Use Pascal's Triangle to complete the expansion of (r + s)^4. r^4 + 4r^3s + ____r^2s^2 + 4rs^3 + s^4

Identify Pascal's Triangle: Pascal's Triangle for the 4th row is 1, 4, 6, 4, 1. These numbers are the coefficients for the expansion.Determine Missing Term: The missing term is the coefficient for r^2s^2, which is the 3rd term in the expansion, so we use the 3rd number in the 4th row of Pascal's Triangle, which is 6.Calculate Complete Expansion: The complete expansion is r^4 + 4r^3s + 6r^2s^2 + 4rs^3 + s^4.

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Use Pascal's Triangle to complete the expansion of $(r + s)^4$ . $\newline$ $r^4 + 4r^3s + \underline{\hspace{2em}}r^2s^2 + 4rs^3 + s^4$

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

(r + s)^4

\newline

r^4 + 4r^3s + \underline{\hspace{2em}}r^2s^2 + 4rs^3 + s^4

Identify Pascal's Triangle: Pascal's Triangle for the $4^{\text{th}}$ row is $1, 4, 6, 4, 1$ . These numbers are the coefficients for the expansion.
Determine Missing Term: The missing term is the coefficient for $r^2s^2$ , which is the $3$ rd term in the expansion, so we use the $3$ rd number in the $4$ th row of Pascal's Triangle, which is $6$ .
Calculate Complete Expansion: The complete expansion is $r^4 + 4r^3s + 6r^2s^2 + 4rs^3 + s^4$ .