To find the first term of the binomial expansion [tex]\((x + y)^4\)[/tex], we can use the binomial theorem. The binomial theorem states that [tex]\((a + b)^n\)[/tex] can be expanded as:
[tex]\[
(a + b)^n = a^n + \binom{n}{1} a^{n-1} b + \binom{n}{2} a^{n-2} b^2 + \cdots + \binom{n}{n-1} a b^{n-1} + b^n
\][/tex]
Here, [tex]\(a = x\)[/tex], [tex]\(b = y\)[/tex], and [tex]\(n = 4\)[/tex]. According to the binomial theorem, the first term of the binomial expansion is [tex]\(a^n\)[/tex].
In our specific case:
1. [tex]\(a = x\)[/tex]
2. [tex]\(n = 4\)[/tex]
Therefore, the first term of the expansion is:
[tex]\[
x^n = x^4
\][/tex]
So, the first term of the binomial expansion [tex]\((x + y)^4\)[/tex] is:
[tex]\[
x^4
\][/tex]
