Math  /  Algebra

QuestionWhich of the expressions below is equal to 3x+9y+153 x+9 y+15 ? Select all that apply. A) 3(x+y+5)3(x+y+5) B) 3(3x+3y)+153(3 x+3 y)+15 C) 3(x+3y+5)3(x+3 y+5) D) 3x+3(3y+5)3 x+3(3 y+5) You can earn 5 coins
A в c D Submit

Studdy Solution

STEP 1

What is this asking? Which expressions are the same as 3x+9y+153x + 9y + 15? Watch out! Don't forget to distribute correctly!
It's a super common mistake, so take your time and double-check your work.

STEP 2

1. Expand A
2. Expand B
3. Expand C
4. Expand D

STEP 3

Let's **expand** option A, which is 3(x+y+5)3(x + y + 5), and see if it matches our original expression.
Remember, expanding means distributing the 33 to each term inside the parentheses.

STEP 4

3(x+y+5)=3x+3y+35=3x+3y+153(x + y + 5) = 3 \cdot x + 3 \cdot y + 3 \cdot 5 = 3x + 3y + 15 Oops, 3x+3y+153x + 3y + 15 doesn't match our **original expression** 3x+9y+153x + 9y + 15, so A is *not* a match.

STEP 5

Now, let's **expand** option B: 3(3x+3y)+153(3x + 3y) + 15.

STEP 6

3(3x+3y)+15=33x+33y+15=9x+9y+153(3x + 3y) + 15 = 3 \cdot 3x + 3 \cdot 3y + 15 = 9x + 9y + 15 Hmm, 9x+9y+159x + 9y + 15 doesn't match our **original expression** 3x+9y+153x + 9y + 15 either.
So, B is *not* correct.

STEP 7

Time to **expand** option C: 3(x+3y+5)3(x + 3y + 5).

STEP 8

3(x+3y+5)=3x+33y+35=3x+9y+153(x + 3y + 5) = 3 \cdot x + 3 \cdot 3y + 3 \cdot 5 = 3x + 9y + 15 Woohoo! 3x+9y+153x + 9y + 15 *matches* our **original expression** 3x+9y+153x + 9y + 15.
C is a winner!

STEP 9

Finally, let's **expand** option D: 3x+3(3y+5)3x + 3(3y + 5).

STEP 10

3x+3(3y+5)=3x+33y+35=3x+9y+153x + 3(3y + 5) = 3x + 3 \cdot 3y + 3 \cdot 5 = 3x + 9y + 15 Wow, another match! 3x+9y+153x + 9y + 15 is the same as our **original expression** 3x+9y+153x + 9y + 15.
D is correct too!

STEP 11

The expressions that are equal to 3x+9y+153x + 9y + 15 are C and D.

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord