Answered

Looking for answers? Westonci.ca is your go-to Q&A platform, offering quick, trustworthy responses from a community of experts. Connect with a community of experts ready to help you find accurate solutions to your questions quickly and efficiently. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.

Applying the Binomial Theorem

In this activity, you'll find the expanded form of the binomial expression [tex]\((x+y)^4\)[/tex] using the binomial theorem. Answer the following questions to expand the binomial expression [tex]\((x+y)^4\)[/tex] using the binomial theorem.

[tex]\[
(a+b)^n = a^n + \frac{n}{1!} a^{n-1} b^1 + \frac{n(n-1)}{2!} a^{n-2} b^2 + \frac{n(n-1)(n-2)}{3!} a^{n-3} b^3 + \cdots + b^n
\][/tex]

Part A
Determine the first term of the binomial expansion [tex]\((x+y)^4\)[/tex].

Sagot :

GinnyAnswer
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]
Thanks for stopping by. We are committed to providing the best answers for all your questions. See you again soon. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Westonci.ca is your go-to source for reliable answers. Return soon for more expert insights.