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Use Pascal's Triangle to complete the expansion of (p+q)5(p + q)^5. \newlinep5+p^5 + ____p4q+10p3q2+10p2q3+5pq4+q5p^4q + 10p^3q^2 + 10p^2q^3 + 5pq^4 + q^5

Full solution

Q. Use Pascal's Triangle to complete the expansion of (p+q)5(p + q)^5. \newlinep5+p^5 + ____p4q+10p3q2+10p2q3+5pq4+q5p^4q + 10p^3q^2 + 10p^2q^3 + 5pq^4 + q^5
  1. Look at Pascal's Triangle: Look at the 6th6^{\text{th}} row of Pascal's Triangle to find the coefficients for the expansion of (p+q)5(p + q)^5.
  2. Identify Coefficients: The 66th row of Pascal's Triangle is 1,5,10,10,5,11, 5, 10, 10, 5, 1. These are the coefficients for the terms from p5p^5 to q5q^5.
  3. Find p4qp^4q Coefficient: The coefficient for the p4qp^4q term is the second number in the 66th row, which is 55.
  4. Write Complete Expansion: Write down the complete expansion with the missing coefficient filled in: p5+5p4q+10p3q2+10p2q3+5pq4+q5p^5 + 5p^4q + 10p^3q^2 + 10p^2q^3 + 5pq^4 + q^5.

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