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The problem in the image asks to find the product of \((3q + 5)(2q^2 + 4q - 3)\) and collect all like terms.

### Step-by-step Solution:

1. **Distribute each term in \((3q + 5)\) to the terms in \((2q^2 + 4q - 3)\):**

   - First, distribute \(3q\):
     \[
     3q \cdot (2q^2 + 4q - 3) = (3q \cdot 2q^2) + (3q \cdot 4q) + (3q \cdot -3)
     \]
     \[
     = 6q^3 + 12q^2 - 9q
     \]

   - Next, distribute \(5\):
     \[
     5 \cdot (2q^2 + 4q - 3) = (5 \cdot 2q^2) + (5 \cdot 4q) + (5 \cdot -3)
     \]
     \[
     = 10q^2 + 20q - 15
     \]

2. **Now, add all the terms together:**
   \[
   6q^3 + 12q^2 - 9q + 10q^2 + 20q - 15
   \]

3. **Combine like terms:**
   - For \(q^3\): \(6q^3\) (no like terms to combine)
   - For \(q^2\): \(12q^2 + 10q^2 = 22q^2\)
   - For \(q\): \(-9q + 20q = 11q\)
   - Constant term: \(-15\)

4. **Final answer:**
   \[
   6q^3 + 22q^2 + 11q - 15
   \]

Would you like any further details or clarifications?

Here are 5 related questions to expand your understanding:
1. How do you simplify the product of two binomials?
2. What is the distributive property and why is it useful in algebra?
3. How do you combine like terms in a polynomial?
4. Can you explain how to factor a cubic expression?
5. What are some real-world applications of polynomial multiplication?

**Tip:** When multiplying polynomials, always distribute each term from the first polynomial to every term in the second polynomial.

Find the product. Collect all like terms. (3q + 5)(2q^2 + 4q - 3)

Learn how to multiply two polynomials, (3q + 5)(2q^2 + 4q - 3), and combine like terms in this detailed, step-by-step algebraic solution. This problem covers essential algebra concepts, such as the distributive property and polynomial multiplication, suitable for students in Grades 8-10.

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