Question

Given the polynomial : (3x+4)^5. find the coefficient of x³ !​

Answer 1

`\displaystyle 4320 {x }^(3)`

Explanation:

to solve binomials like this there's a way called binomial theorem given by

`\displaystyle {(a + b)}^(n) = \sum _(k = 0) ^(n) \binom{n}{k} {a}^(n - k) {b}^(k)`

but for this question we need the following part

`\displaystyle \boxed{ \binom{n}{k} {a}^(n - k) {b}^(k) }`

from the question we obtain that a,b and n is 3x,4 and 5 since we want to find the coefficient x³ k should be (5-3) = 2 so we have determined the variables now just substitute

`\displaystyle \binom{5}{2} {(3x)}^(5 - 2) \cdot {4}^(2)`

simplify which yields:

`\displaystyle \boxed{ \bold{4320 {x }^(3)} }`

and we are done!