Factor the polynomial by grouping nm - np + 2m - 2p

To factor the polynomial \( nm - np + 2m - 2p \) by grouping, follow these steps:

1. **Group terms**: 
   Group the terms in pairs to simplify the factoring process:
   \[
   (nm - np) + (2m - 2p)
   \]

2. **Factor out the common factors** in each group:
   - In the first group, \( nm - np \), factor out \( n \):
     \[
     n(m - p)
     \]
   - In the second group, \( 2m - 2p \), factor out \( 2 \):
     \[
     2(m - p)
     \]

   So, the expression now looks like:
   \[
   n(m - p) + 2(m - p)
   \]

3. **Factor out the common binomial factor** \( (m - p) \):
   \[
   (m - p)(n + 2)
   \]

Therefore, the factored form of the polynomial \( nm - np + 2m - 2p \) is:

\[
(m - p)(n + 2)
\]

Would you like further details or have any questions about the steps? 

Here are 5 related questions that expand on this information:

1. How do you factor a polynomial when there are more than two groups?
2. What is the significance of factoring in solving polynomial equations?
3. How can you check if the factorization of a polynomial is correct?
4. What are some common factoring techniques other than grouping?
5. How would you factor a polynomial with more than two variables?

**Tip:** Always check your factored expression by expanding it to ensure it matches the original polynomial!

Learn how to factor the polynomial nm - np + 2m - 2p using the grouping method with a detailed step-by-step solution. This problem covers key algebraic concepts, including polynomials and factoring techniques. 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