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

Question

Group the expressions that have the same value.

  1. (b+c)(a4) (b+c)(a-4)

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

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

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

    a. ac+ab4b4c ac+ab-4b-4c

    b. 4b+ab4cac 4b+ab-4c-ac

    c. bcab+4c4a bc-ab+4c-4a

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

Video Solution

Step-by-Step Solution

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)(a4) (b+c)(a-4)

  • Apply distributive property: ba4b+ca4c ba - 4b + ca - 4c
  • Combine like terms, resulting in: ab+ac4b4c ab + ac - 4b - 4c .
  • This matches with option a: ac+ab4b4c ac + ab - 4b - 4c .

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

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

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

  • Apply distributive property: abac+4b4c ab - ac + 4b - 4c
  • Combine like terms, resulting in: abac+4b4c ab - ac + 4b - 4c .
  • This matches with option b: 4b+ab4cac 4b + ab - 4c - ac .

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

  • Apply distributive property: bcba+4c4a bc - ba + 4c - 4a
  • Combine like terms, resulting in: bcab+4c4a bc - ab + 4c - 4a .
  • This matches with option c: bcab+4c4a 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.

Answer

1-a, 2-d, 3-b, 4-c