Use Pascal's triangle to expand binomial

(2x + 3) ^4

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

Step-by-step 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