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Answer :
We start with the areas of the two rooms:
- Living room area: [tex]$54$[/tex] square feet
- Bedroom area: [tex]$42$[/tex] square feet
Step 1. Find the greatest common factor (GCF).
The GCF of [tex]$54$[/tex] and [tex]$42$[/tex] is [tex]$6$[/tex].
Step 2. Express each area as a product involving the GCF.
Divide each area by [tex]$6$[/tex]:
- For the living room:
[tex]$$54 \div 6 = 9,$$[/tex]
so [tex]$54$[/tex] can be written as [tex]$6 \cdot 9$[/tex].
- For the bedroom:
[tex]$$42 \div 6 = 7,$$[/tex]
so [tex]$42$[/tex] can be written as [tex]$6 \cdot 7$[/tex].
Step 3. Write the expression for the total area factoring out the GCF.
Substitute the factored forms into the sum:
[tex]$$
54 + 42 = (6 \cdot 9) + (6 \cdot 7).
$$[/tex]
Thus, the expression that shows each term with the GCF as one of the factors is:
[tex]$$
(6 \cdot 9) + (6 \cdot 7).
$$[/tex]
- Living room area: [tex]$54$[/tex] square feet
- Bedroom area: [tex]$42$[/tex] square feet
Step 1. Find the greatest common factor (GCF).
The GCF of [tex]$54$[/tex] and [tex]$42$[/tex] is [tex]$6$[/tex].
Step 2. Express each area as a product involving the GCF.
Divide each area by [tex]$6$[/tex]:
- For the living room:
[tex]$$54 \div 6 = 9,$$[/tex]
so [tex]$54$[/tex] can be written as [tex]$6 \cdot 9$[/tex].
- For the bedroom:
[tex]$$42 \div 6 = 7,$$[/tex]
so [tex]$42$[/tex] can be written as [tex]$6 \cdot 7$[/tex].
Step 3. Write the expression for the total area factoring out the GCF.
Substitute the factored forms into the sum:
[tex]$$
54 + 42 = (6 \cdot 9) + (6 \cdot 7).
$$[/tex]
Thus, the expression that shows each term with the GCF as one of the factors is:
[tex]$$
(6 \cdot 9) + (6 \cdot 7).
$$[/tex]
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