Math  /  Algebra

QuestionMock/Practice Thst 8 (eptional) Question 18 of 20 (1) poin) I Gueatlon Attempts 1 of 1 Time Remaining: 144 1 2 3 4 5 6 7 8 9 10 11 12
The formula P=2a+2bP=2 a+2 b represents the perimeter, PP, of a parallelogram given the base, bb, and an adjacent side, aa. Factor out the GCF and write an equivalent formula in factored form. PP \equiv \square Continue Submit Assig 2024 MeGraw HIIILC. All Righte Reserved. Torms of Use Privagy Center

Studdy Solution

STEP 1

What is this asking? We're given a formula for the perimeter of a parallelogram and need to rewrite it by factoring out the greatest common factor. Watch out! Don't forget to check your factored form by distributing it back – it should match the original formula!

STEP 2

1. Identify the GCF.
2. Factor out the GCF.

STEP 3

Alright, let's look at our formula: P=2a+2bP = 2a + 2b.
We need to find the **greatest common factor (GCF)** of the terms 2a2a and 2b2b.
What's the biggest thing they both have in common?

STEP 4

Well, 2a2a is 2a2 \cdot a and 2b2b is 2b2 \cdot b.
They both have a factor of **2**!
So, our **GCF is 2**!
Woohoo!

STEP 5

Now, let's **factor out** that **2**.
Think of it like this: we're dividing each term by the GCF and putting it outside a set of parentheses.

STEP 6

So, we have P=2a+2bP = 2a + 2b.
Dividing 2a2a by **2** gives us aa.
Dividing 2b2b by **2** gives us bb.

STEP 7

We put the **GCF (2)** outside the parentheses and the results of our divisions inside: P=2(a+b)P = 2(a + b).
Boom!

STEP 8

Let's double-check!
Distribute the **2** back into the parentheses: 2a+2b=2a+2b2 \cdot a + 2 \cdot b = 2a + 2b.
It matches our original formula, so we're golden!

STEP 9

Our equivalent formula in factored form is P=2(a+b)P = 2(a + b).

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