Find the product.

left parenthesis 8 x minus 5 right parenthesis left parenthesis 9 x plus 4 right parenthesis(8x−5)(9x+4)

Question content area bottom

Part 1

left parenthesis 8 x minus 5 right parenthesis left parenthesis 9 x plus 4 right parenthesis(8x−5)(9x+4)equals=enter your response here

To find the product \((8x - 5)(9x + 4)\), we will use the distributive property to multiply each term in the first expression by each term in the second expression.

### Step-by-Step Solution:

1. **Distribute \(8x\) to each term in the second polynomial:**
   \[
   8x \cdot (9x + 4) = 8x \cdot 9x + 8x \cdot 4
   \]
   Simplifying this, we get:
   \[
   72x^2 + 32x
   \]

2. **Distribute \(-5\) to each term in the second polynomial:**
   \[
   -5 \cdot (9x + 4) = -5 \cdot 9x + -5 \cdot 4
   \]
   Simplifying this, we get:
   \[
   -45x - 20
   \]

3. **Combine all the terms:**
   \[
   72x^2 + 32x - 45x - 20
   \]

4. **Simplify by combining like terms:**
   \[
   72x^2 - 13x - 20
   \]

### Final Answer:
\[
(8x - 5)(9x + 4) = 72x^2 - 13x - 20
\]

Would you like more details or have any questions about the solution?

Here are 5 related questions to further your understanding:

1. What is the product of \((2x + 3)(3x - 7)\)?
2. How do you factor the expression \(72x^2 - 13x - 20\)?
3. What happens if you multiply \((8x - 5)(x + 4)\)?
4. How do you expand \((5x - 2)(2x^2 + 3x - 1)\)?
5. What is the result of multiplying \((4x + 1)(9x - 2)\)?

**Tip:** Always carefully combine like terms after distributing to ensure that the expression is fully simplified.

Learn how to find the product of (8x - 5)(9x + 4) step-by-step with detailed calculations and explanations. This problem involves polynomial multiplication and the distributive property, suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation