Final answer:
To factor the algebraic expression ab+bc-am-cm by grouping, group similar terms, factor out common factors from each group, and rewrite the expression as (a+c)(b-m), where (a+c) is the common factor.
Step-by-step explanation:
- The problem asks for factorization by grouping of the algebraic expression ab+bc-am-cm. The process involves two main steps.
- First, we need to group terms with common factors, and then we need to factor out these common factors.
- Let's group the terms as follows: (ab+bc) + (-am-cm). Now, within each group, we can factor out the common factors.
- From the first group (ab+bc), we can factor out 'b', giving us b(a+c).
- From the second group (-am-cm), we can factor out '-m', giving us -m(a+c).
- The expression is now written as b(a+c) - m(a+c).
- With both terms now containing the common factor (a+c), we can factor this out.
- The final factored form of the expression is (a+c)(b-m).