Math  /  Algebra

QuestionChoose the equivalent expression for the given expression: 2(r+y)2(r+y) 3ry3 r y 2r+y2 r+y 2r+2y2 r+2 y 3r+3y3 r+3 y

Studdy Solution

STEP 1

What is this asking? We need to find which expression is the same as 2(r+y)2(r+y). Watch out! Don't forget to multiply *both* rr and yy by **2**!

STEP 2

1. Expand the Expression
2. Identify the Equivalent Expression

STEP 3

Alright, let's **expand** this expression!
We have 2(r+y)2(r+y).
This means we multiply **2** by *each* term inside the parentheses.
It's like the **2** wants to play with *both* rr and yy!

STEP 4

So, first, we multiply **2** by rr, which gives us 2r=2r2 \cdot r = 2r.

STEP 5

Next, we multiply **2** by yy, which gives us 2y=2y2 \cdot y = 2y.

STEP 6

Now, we **add** these two results together: 2r+2y2r + 2y.
This is the **expanded form**!

STEP 7

Let's look at our options.
We're looking for an expression that matches our **expanded form**, 2r+2y2r + 2y.

STEP 8

Is it 3ry3ry?
Nope, that's multiplication, not addition!

STEP 9

Is it 2r+y2r + y?
Close, but it's missing the **2** in front of the yy.

STEP 10

Is it 2r+2y2r + 2y?
YES! This is a perfect match!

STEP 11

Is it 3r+3y3r + 3y?
Nope, the numbers are wrong.
We need **2**'s, not **3**'s.

STEP 12

The equivalent expression is 2r+2y2r + 2y.

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