Math  /  Algebra

QuestionThese algebraic tiles represent the expression 5(x+2)5(x+2).
Which expression is equivalent to 5(x+2)5(x+2) ? 5x+105 x+10 15x15 x 10x+510 x+5 5x105 x-10
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Studdy Solution

STEP 1

What is this asking? We're asked to simplify the expression 5(x+2)5(x+2) using the distributive property, which basically means figuring out what's 55 times xx *plus* 22. Watch out! Don't forget to multiply *both* terms inside the parentheses by 55!
It's easy to accidentally only multiply the xx and forget about the 22.

STEP 2

1. Distribute the 5
2. Simplify

STEP 3

Alright, let's **distribute** that 55 across the terms inside the parentheses!
This means we'll multiply *both* the xx and the 22 by 55.
Think of it like sharing the 55 with everyone at the party inside the parentheses!

STEP 4

So, we have 55 times xx, which gives us 5x5 \cdot x, or just 5x5x.

STEP 5

Then, we have 55 times 22, which gives us 52=105 \cdot 2 = 10.

STEP 6

Now, we put these two parts back together with the **plus sign** that was originally inside the parentheses.
This gives us 5x+105x + 10.

STEP 7

Look at that!
Our expression 5x+105x + 10 is already simplified!
There are no like terms to combine, so we're done.
High five!

STEP 8

The equivalent expression is 5x+105x + 10.

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