Question

Expand the binomials using the Binomial theorem.
(2x+3y)^4

Answer 1

binomial theorem says

\[(a + b)^n = \left(\begin{matrix}n \\ r\end{matrix}\right) \sum_{n = 0}^{k}(a)^{n - k}(b)^k\]

Answer 2

how do I figure it out

Answer 3

ok... so a = 2x and b = 3y and n = 4

so rather than using combinations to get the initial coefficient you can just use Pascal's Triangle

so its 1, 4, 6, 4, 1

so the then terms are

\[1 \times (2x)^4(3y)^0 + 4 \times (2x)^4(3y)^1 + 6 \times (2x)^3 (3y)^2+...\]

so as the power of (2x) decreases the power of (3y) increases...

there are 5 terms... so when you have all 5 just multiply the coefficients

\[16x^4 + 4 \times 8x^3\times2y+ ..... \]

Answer 4

hope it makes sense

Answer 5

yea thank you

Answer 6

opps I think I got the powers and sum from and to.. round the wrong way

Answer 7

what do you mean?