Ad - bc - bd + ac factor the polynomial by grouping 

To factor the polynomial \( Ad - bc - bd + ac \) by grouping, follow these steps:

1. **Group terms**: 
   Group the terms in pairs to simplify the factoring process:
   \[
   (Ad - bd) + (-bc + ac)
   \]

2. **Factor out the common factors** in each group:
   - In the first group, \( Ad - bd \), factor out \( d \):
     \[
     d(A - b)
     \]
   - In the second group, \( -bc + ac \), factor out \( c \):
     \[
     c(-b + a)
     \]

   Rewrite the second group by rearranging \( -b + a \) as \( a - b \), thus:
   \[
   c(a - b)
   \]

   So, the expression now looks like:
   \[
   d(A - b) + c(a - b)
   \]

3. **Factor out the common binomial factor** \( (A - b) \):
   \[
   (A - b)(d + c)
   \]

Therefore, the factored form of the polynomial \( Ad - bc - bd + ac \) is:

\[
(d + c)(A - b)
\]

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 determine which terms to group when factoring by grouping?
2. Can all polynomials be factored by grouping? Why or why not?
3. What is the role of factoring in simplifying algebraic expressions?
4. How can factoring by grouping help in solving equations?
5. How does factoring polynomials relate to finding their roots?

**Tip:** When factoring by grouping, always rearrange terms if necessary to identify groups with common factors easily!

Learn how to factor the polynomial Ad - bc - bd + ac by grouping. Follow a step-by-step solution involving grouping terms, factoring out common factors, and identifying binomial factors. 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