Use Pascal's Triangle to complete the expansion of (p + q)^5. p^5 + ____p^4q + 10p^3q^2 + 10p^2q^3 + 5pq^4 + q^5

Look at Pascal's Triangle: Look at the 6th row of Pascal's Triangle to find the coefficients for the expansion of (p + q)^5. Identify Coefficients: The 6th row of Pascal's Triangle is 1, 5, 10, 10, 5, 1. These are the coefficients for the terms from p^5 to q^5. Find p^4q Coefficient: The coefficient for the p^4q term is the second number in the 6th row, which is 5. Write Complete Expansion: Write down the complete expansion with the missing coefficient filled in: p^5 + 5p^4q + 10p^3q^2 + 10p^2q^3 + 5pq^4 + q^5.

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Use Pascal's Triangle to complete the expansion of $(p + q)^5$ . $\newline$ $p^5 +$ ____ $p^4q + 10p^3q^2 + 10p^2q^3 + 5pq^4 + q^5$

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Precalculus

Pascal's triangle and the Binomial Theorem

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

(p + q)^5

\newline

p^5 +

____

p^4q + 10p^3q^2 + 10p^2q^3 + 5pq^4 + q^5

Look at Pascal's Triangle: Look at the $6^{\text{th}}$ row of Pascal's Triangle to find the coefficients for the expansion of $(p + q)^5$ .
Identify Coefficients: The $6$ th row of Pascal's Triangle is $1, 5, 10, 10, 5, 1$ . These are the coefficients for the terms from $p^5$ to $q^5$ .
Find $p^4q$ Coefficient: The coefficient for the $p^4q$ term is the second number in the $6$ th row, which is $5$ .
Write Complete Expansion: Write down the complete expansion with the missing coefficient filled in: $p^5 + 5p^4q + 10p^3q^2 + 10p^2q^3 + 5pq^4 + q^5$ .