In the expansion of (2a+4b)⁸ the possible variable terms are a⁸, a⁵b³, a³b⁵, a⁷b, and b⁸.
What is an Expression?
In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The expansion is given by the following formula: [tex]\left(a + b\right)^{n} = \sum_{k=0}^{n} {\binom{n}{k}} a^{n - k} b^{k}[/tex], where [tex]{\binom{n}{k}} = \frac{n!}{\left(n - k\right)! k!}[/tex]
As given to us, a = 2a, b = 4 b, and n = 8.
Therefore, [tex]\left(2 a + 4 b\right)^{8} = \sum_{k=0}^{8} {\binom{8}{k}} \left(2 a\right)^{8 - k} \left(4 b\right)^{k}(2a+4b)[/tex].
Thus, [tex]\left(2 a + 4 b\right)^{8} = 256 a^{8} + 4096 a^{7} b + 28672 a^{6} b^{2} + 114688 a^{5} b^{3} + 286720 a^{4} b^{4} + 458752 a^{3} b^{5} + 458752 a^{2} b^{6} + 262144 a b^{7} + 65536 b^{8}.[/tex]
Hence, In the expansion of (2a+4b)⁸ the possible variable terms are a⁸, a⁵b³, a³b⁵, a⁷b, and b⁸.
Learn more about Expression:
https://brainly.com/question/13947055
#SPJ1
