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To solve the problem, we need to find the 8th term of the binomial expansion of \((x + y)^{10}\).

The general term of a binomial expansion \((x + y)^n\) is given by:

\[
T_{k+1} = \binom{n}{k} x^{n-k} y^k
\]

Where:
- \( n = 10 \) (from \((x + y)^{10}\)),
- \( k \) is the index for the term you want (for the 8th term, \( k = 7 \), since \( T_{k+1} \) gives the \( (k+1) \)-th term),
- \( \binom{n}{k} \) is the binomial coefficient.

Now, substituting \( n = 10 \) and \( k = 7 \):

\[
T_8 = \binom{10}{7} x^{10-7} y^7 = \binom{10}{7} x^3 y^7
\]

First, calculate the binomial coefficient:

\[
\binom{10}{7} = \binom{10}{3} = \frac{10 \times 9 \times 8}{3 \times 2 \times 1} = 120
\]

Thus, the 8th term is:

\[
T_8 = 120 x^3 y^7
\]

From the given answer choices, the correct answer is:

**120 \(x^3 y^7\)**, which is the second option.

Would you like more details or further clarification?

Here are 5 related questions to deepen your understanding:

1. What is the general term formula for the binomial expansion of \((a + b)^n\)?
2. How do you calculate a binomial coefficient \(\binom{n}{k}\) without using a calculator?
3. What is the 5th term in the binomial expansion of \((x + y)^{12}\)?
4. How does the power of \(x\) and \(y\) change in each term of a binomial expansion?
5. Can binomial expansion be used for negative or fractional exponents?

**Tip**: The sum of the powers of \(x\) and \(y\) in any term of a binomial expansion always equals the original exponent \(n\).

What is the 8th term of the binomial expansion (x + y)^10? Select the correct answer.

Learn how to calculate the 8th term in the binomial expansion of (x + y)^10 using the binomial theorem. This detailed solution covers key algebraic concepts and the application of the binomial coefficient formula. Suitable for students in Grades 10-12.

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