Answered

At Westonci.ca, we provide clear, reliable answers to all your questions. Join our vibrant community and get the solutions you need. Discover solutions to your questions from experienced professionals across multiple fields on our comprehensive Q&A platform. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.

Write each expression as the product of two polynomials.

[tex]\[ a(b-c) + d(c-b) \][/tex]

Sagot :

GinnyAnswer
Certainly! Let's start by understanding the given expression and then simplify and factor it step-by-step.

Given expression:
[tex]\[ a(b - c) + d(c - b) \][/tex]

1. Identify the structure:
We notice that the expression consists of two terms:
- The first term is [tex]\( a(b - c) \)[/tex]
- The second term is [tex]\( d(c - b) \)[/tex]

2. Rewriting the second term:
Notice that [tex]\( d(c - b) \)[/tex] can be rewritten as [tex]\( d(-1)(b - c) \)[/tex], which simplifies to [tex]\( -d(b - c) \)[/tex].

Thus, the expression becomes:
[tex]\[ a(b - c) + (-d)(b - c) \][/tex]
[tex]\[ a(b - c) - d(b - c) \][/tex]

3. Factor out the common term:
We see that [tex]\( (b - c) \)[/tex] is a common factor in both terms. So, we can factor [tex]\( (b - c) \)[/tex] out from the expression:

Factor out [tex]\( (b - c) \)[/tex]:
[tex]\[ (b - c)(a - d) \][/tex]

Therefore, the expression [tex]\( a(b - c) + d(c - b) \)[/tex] can be written as the product of two polynomials:
[tex]\[ (a - d)(b - c) \][/tex]
Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.