Matching Expressions: Group (b+c)(a-4) and Similar Polynomial Products

Group the expressions that have the same value.

1. $(b+c)(a-4)$

2. $(4+c)(a+b)$

3. $(a+4)(b-c)$

4. $(b+4)(c-a)$

   a. $ac+ab-4b-4c$

   b. $4b+ab-4c-ac$

   c. $bc-ab+4c-4a$

   d. $4a+4b+ac+cb$

To solve this problem, we need to expand each given algebraic expression using the distributive property and match each expanded form with the given standard forms. Let’s go through each expression:

Expression 1: $(b+c)(a-4)$

• Apply distributive property: $ba - 4b + ca - 4c$
• Combine like terms, resulting in: $ab + ac - 4b - 4c$.
• This matches with option a: $ac + ab - 4b - 4c$.

Expression 2: $(4+c)(a+b)$

• Apply distributive property: $4a + 4b + ca + cb$
• Combine like terms, resulting in: $4a + 4b + ac + cb$.
• This matches with option d: $4a + 4b + ac + cb$.

Expression 3: $(a+4)(b-c)$

• Apply distributive property: $ab - ac + 4b - 4c$
• Combine like terms, resulting in: $ab - ac + 4b - 4c$.
• This matches with option b: $4b + ab - 4c - ac$.

Expression 4: $(b+4)(c-a)$

• Apply distributive property: $bc - ba + 4c - 4a$
• Combine like terms, resulting in: $bc - ab + 4c - 4a$.
• This matches with option c: $bc - ab + 4c - 4a$.

Grouping the results, we have:

• 1 matches with a.
• 2 matches with d.
• 3 matches with b.
• 4 matches with c.

Therefore, the solution to the problem is 1-a, 2-d, 3-b, 4-c.