I see the image contains a set of math problems related to Pascal’s triangle, binomial expansions, and general binomial theorem topics.

Here’s a breakdown of some of the questions visible in the image:

1. The first problem asks to find the value of $a, b, c, d, e, f$ given the expression $\binom{12}{6} = abcdef.$
2. The second problem is to expand $(x + 2y)^5$ fully.
3. There are tasks involving Pascal’s triangle and finding specific terms in binomial expansions, using both Pascal’s triangle and the binomial theorem.
4. Another problem asks for the expansion of binomials like $(1 + 2x)^7$, $(x + 3y)^6$, $(x + y)^8$, etc.
5. The last problem asks for the coefficient of the 4th term in the expansion of $(x - \frac{1}{2} y)^9$.

Would you like me to solve one of these specific problems or explain the methods involved in solving them (e.g., using Pascal’s triangle or the binomial theorem)? Let me know!

Here are some related questions to consider:

1. How do you compute binomial coefficients using Pascal’s triangle?
2. What is the general form of the binomial expansion?
3. How do you identify the middle term in a binomial expansion?
4. What is the significance of using the binomial theorem for large powers?
5. How can the binomial theorem be applied to real-world problems?

Tip: For easier expansion of binomials, remember that the coefficients follow a pattern based on Pascal’s triangle, and terms are determined by decreasing powers of the first variable and increasing powers of the second.