Question

Use Pascal’s triangle to expand binomial

(2x + 3)^4

Answer 1

16x^4 +96x^3 +216x^2 +216x +81

Explanation:

The relevant row of Pascal's triangle is the one with 4 as the second number. That corresponds to the power of the binomial being expanded. The numbers on that row multiply the term a^(4-k)·b^k of the expansion of (a+b)^4 as k varies from 0 to 4.

WIth the multiplier of Pascal's triangle, the terms are ...

1·(2x)^4 + 4·(2x)^3·(3) + 6·(2x)^2·(3)^2 + 4·(2x)·(3)^3 + 1·(3)^4

= 16x^4 +96x^3 +216x^2 +216x +81