Group the expressions that have the same value.
(b+c)(a−4)
(4+c)(a+b)
(a+4)(b−c)
(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.