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Use Pascal's Triangle to complete the expansion of (t+u)4(t + u)^4. \newlinet4+t^4 + ____t3u+6t2u2+4tu3+u4t^3u + 6t^2u^2 + 4tu^3 + u^4

Full solution

Q. Use Pascal's Triangle to complete the expansion of (t+u)4(t + u)^4. \newlinet4+t^4 + ____t3u+6t2u2+4tu3+u4t^3u + 6t^2u^2 + 4tu^3 + u^4
  1. Pascal's Triangle Coefficients: Pascal's Triangle for the 44th row is 1,4,6,4,11, 4, 6, 4, 1. These numbers are the coefficients for the expansion.
  2. Determining Second Term: The second term in the expansion is t3t^3 times uu, so we use the second coefficient from Pascal's Triangle, which is 44.
  3. Expansion of (t+u)4(t + u)^4: The expansion of (t+u)4(t + u)^4 is t4+4t3u+6t2u2+4tu3+u4t^4 + 4t^3u + 6t^2u^2 + 4tu^3 + u^4.

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