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Use Pascal's Triangle to complete the expansion of (r+s)4(r + s)^4. \newliner4+4r3s+‾r2s2+4rs3+s4r^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(r + s)^4. \newliner4+4r3s+‾r2s2+4rs3+s4r^4 + 4r^3s + \underline{\hspace{2em}}r^2s^2 + 4rs^3 + s^4
  1. Identify Pascal's Triangle: Pascal's Triangle for the 4th4^{\text{th}} row is 1,4,6,4,11, 4, 6, 4, 1. These numbers are the coefficients for the expansion.
  2. Determine Missing Term: The missing term is the coefficient for r2s2r^2s^2, which is the 33rd term in the expansion, so we use the 33rd number in the 44th row of Pascal's Triangle, which is 66.
  3. Calculate Complete Expansion: The complete expansion is r4+4r3s+6r2s2+4rs3+s4r^4 + 4r^3s + 6r^2s^2 + 4rs^3 + s^4.

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