Simplify the Expression: 7z+10b+2bz+35 Using Like Terms

Question

Which of the expressions is equivalent to the expression?

7z+10b+2bz+35 7z+10b+2bz+35

Video Solution

Step-by-Step Solution

To solve this problem, we'll focus on factorization by grouping:

  • Step 1: Identify groupable terms in 7z+10b+2bz+35 7z + 10b + 2bz + 35 .
  • Step 2: Reorganize and group terms for greatest common factor extraction.
  • Step 3: Factor each group and simplify.

Now, let's work through each step:

Step 1:
Observe that we can reorganize the expression to facilitate grouping:

7z+35+10b+2bz 7z + 35 + 10b + 2bz .

Step 2:
Group into pairs: (7z+35)+(10b+2bz)(7z + 35) + (10b + 2bz).
Within each pair, extract common factors:

=7(z+5)+2b(z+5)= 7(z + 5) + 2b(z + 5), noticing that each group factors nicely.

Step 3:
Since both terms now have a common factor of (z+5)(z + 5), we can factor it out:

=(7+2b)(z+5)= (7 + 2b)(z + 5).

Therefore, the expression 7z+10b+2bz+35 7z + 10b + 2bz + 35 is equivalent to (7+2b)(z+5)(7 + 2b)(z + 5).

This matches choice 1: (7+2b)(z+5) (7+2b)(z+5) .

Answer

(7+2b)(z+5) (7+2b)(z+5)