https://r2.erweima.ai/mathbot/image/1726663144335nsn8lgvu.jpg

Let's solve the expression \((n - 4)(4n + 2)\) by expanding and simplifying it.

### Step-by-step solution:
1. Use the distributive property (FOIL method):
   \[
   (n - 4)(4n + 2) = n(4n + 2) - 4(4n + 2)
   \]
2. Now, distribute each term:
   \[
   n(4n + 2) = n \cdot 4n + n \cdot 2 = 4n^2 + 2n
   \]
   \[
   -4(4n + 2) = -4 \cdot 4n - 4 \cdot 2 = -16n - 8
   \]
3. Combine like terms:
   \[
   4n^2 + 2n - 16n - 8 = 4n^2 - 14n - 8
   \]

### Final simplified expression:
\[
4n^2 - 14n - 8
\]

This is the simplified product of \((n - 4)(4n + 2)\).

Would you like more details on any part of the solution?

### Related questions:
1. What is the distributive property, and how is it used in algebra?
2. How can we apply the FOIL method to binomials?
3. Can you expand more complex polynomials, such as trinomials?
4. What are like terms, and why do we combine them?
5. How would the process change if the binomials had more complicated terms?

**Tip:** Always simplify the terms after distributing by combining like terms to achieve a cleaner final expression!

Find the product. Simplify your answer. (n - 4)(4n + 2)

Learn how to simplify the product of two binomials (n - 4)(4n + 2) using the distributive property. This step-by-step guide helps students understand key algebraic concepts such as expanding binomials and combining like terms. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation