Question

use pascals triangle to expand ((3s + 2)^5). ((3s + 2)^5 = square)

Explanation:

Step1: Get Pascal's coefficients

For exponent 5, coefficients are $1, 5, 10, 10, 5, 1$

Step2: Apply binomial expansion formula

The binomial expansion is $\sum_{k=0}^{5} \binom{5}{k} (3s)^{5-k}(2)^k$

Step3: Calculate each term

Term 1 ($k=0$): $1 \cdot (3s)^5 \cdot 2^0 = 243s^5$
Term 2 ($k=1$): $5 \cdot (3s)^4 \cdot 2^1 = 5 \cdot 81s^4 \cdot 2 = 810s^4$
Term 3 ($k=2$): $10 \cdot (3s)^3 \cdot 2^2 = 10 \cdot 27s^3 \cdot 4 = 1080s^3$
Term 4 ($k=3$): $10 \cdot (3s)^2 \cdot 2^3 = 10 \cdot 9s^2 \cdot 8 = 720s^2$
Term 5 ($k=4$): $5 \cdot (3s)^1 \cdot 2^4 = 5 \cdot 3s \cdot 16 = 240s$
Term 6 ($k=5$): $1 \cdot (3s)^0 \cdot 2^5 = 32$

Step4: Sum all terms

Add the calculated terms together.

Answer:

$243s^5 + 810s^4 + 1080s^3 + 720s^2 + 240s + 32$