Find the product.
​(xplus3​)(xsquaredminus3xplus9​)
Question content area bottom
Part 1
​(xplus3​)(xsquaredminus3xplus9​)equals
  
enter your response here  ​(Simplify your​ answer.)

To find the product \((x + 3)(x^2 - 3x + 9)\), we can use the distributive property (also known as the FOIL method for binomials). Here, we'll distribute each term in the first expression \(x + 3\) to each term in the second expression \(x^2 - 3x + 9\).

### Step-by-Step Solution:

1. **Distribute \(x\) to each term in the second polynomial:**
   \[
   x \cdot (x^2 - 3x + 9) = x \cdot x^2 - x \cdot 3x + x \cdot 9
   \]
   Simplifying this, we get:
   \[
   x^3 - 3x^2 + 9x
   \]

2. **Distribute \(3\) to each term in the second polynomial:**
   \[
   3 \cdot (x^2 - 3x + 9) = 3 \cdot x^2 - 3 \cdot 3x + 3 \cdot 9
   \]
   Simplifying this, we get:
   \[
   3x^2 - 9x + 27
   \]

3. **Combine all the terms:**
   \[
   x^3 - 3x^2 + 9x + 3x^2 - 9x + 27
   \]

4. **Simplify by combining like terms:**
   \[
   x^3 + 0x^2 + 0x + 27
   \]
   So the final simplified expression is:
   \[
   x^3 + 27
   \]

### Final Answer:
\[
(x + 3)(x^2 - 3x + 9) = x^3 + 27
\]

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

Here are 5 related questions to further your understanding:

1. How do you factorize the expression \(x^3 + 27\)?
2. What is the result of multiplying \((x - 2)(x^2 + 2x + 4)\)?
3. How does the distributive property work with three or more terms?
4. What happens if you expand \((x + 3)^3\)?
5. How do you simplify the expression \((2x + 5)(x^2 - 3x + 2)\)?

**Tip:** When multiplying polynomials, always distribute each term from the first polynomial to every term in the second polynomial to ensure all possible products are accounted for.

Learn how to simplify the product of polynomials (x + 3)(x^2 - 3x + 9) with a detailed step-by-step solution. This problem covers key concepts including polynomials, distributive property, and FOIL method. Suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation