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I can help solve the problems from the image. Here's an overview of the questions, and we can tackle them one at a time.

### Problem Summary:

1. **Binomial Expansion Coefficients**: Find the coefficient of \( x^3 \) in several binomial expansions.
2. **Coefficients in Binomial Expansions**:
   - \( x^2 \) coefficient of \( (2 + ax)^6 \) (find values of \( a \)).
   - \( x^3 \) coefficient in the expansion of \( (3 + bx)^5 = -720 \) (find \( b \)).
   - \( x^3 \) coefficient in \( (2 + x)^3(3 - ax)^4 = 30 \) (find values of \( a \)).
3. **Coefficient Comparisons in Expansions**:
   - In \( (1 - 2xy)^6 \), the coefficient of \( x^2 \) is 40. Use this to find the value of constant \( p \), and the coefficients of \( x \) and \( x^3 \).
   - Several problems involving finding first three terms in binomial expansions and comparing coefficients.

### How would you like to proceed? Would you like detailed steps for any specific question? If so, please let me know which one.

I'll list five related questions based on the binomial expansion topic:

1. What is the general formula for the binomial expansion of \( (a + b)^n \)?
2. How do you find the coefficient of a specific term in a binomial expansion?
3. What is the relationship between binomial coefficients and Pascal’s triangle?
4. How do you calculate the coefficients when expanding a binomial with two variables, such as \( (1 + ax)^n \)?
5. How are coefficients of middle terms affected when \( n \) is even versus odd in a binomial expansion?

### Tip:
When solving binomial expansion problems, remember that the term containing \( x^k \) is given by \( \binom{n}{k} a^{n-k} b^k \), where \( \binom{n}{k} \) is the binomial coefficient.

Find the coefficient of x^3 in the binomial expansions and solve various problems related to binomial expansion coefficients.

Learn how to find the coefficient of x^3 in various binomial expansions with examples. This guide covers key mathematical concepts like binomial theorem, binomial coefficients, and polynomial expansions. Suitable for high school students in grades 10-12.

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