Question

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

Answer 1

Answer:

$\displaystyle 4320 {x }^{3}$

Step-by-step 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!