Question

Find the first 3 terms in the expansion of (2 + 3x)^5 in ascending powers of x..

Answer 1

The first three terms of the expansion of (2 + 3x)^5 using the binomial theorem are 32, 240x, and 720x^2.

Step-by-step explanation:

To find the first 3 terms in the expansion of (2 + 3x)^5, we apply the binomial theorem. This theorem allows us to expand binomials raised to a power in the form of a series. The binomial expansion of (a + b)^n is given by:

a^n + n*a^(n-1)*b + n(n-1)/2!*a^(n-2)*b^2 + ...

In this case, a=2, b=3x, and n=5. Applying the formula, the first three terms of the expansion are:

1. (2)^5 = 32,
2. 5*(2)^4*(3x) = 5*16*3x = 240x, and
3. 5*(4)/2*(2)^3*(3x)^2 = 10*8*9x^2 = 720x^2.

Therefore, the first three terms of the expansion are 32, 240x, and 720x^2.