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

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.