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45 votes
45 votes
An expression is shown below.

6ab^2 + 9a^2b
Which of the following shows an equivalent expression?

An expression is shown below. 6ab^2 + 9a^2b Which of the following shows an equivalent-example-1
User Dzejms
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3.1k points

2 Answers

9 votes
9 votes

Hi! I'm happy to help!

To first solve this, Let's see if we can simplify our expressions using the order of operations: our original expression cannot be simplified. The first expression cannot be simplified. The second expression we can multiply the outside by the parenthesis by the inside, same with the third and fourth.

(make sure everything outside of the parenthesis is being multiplied by each part inside of the parenthesis)

9a²b²

9a²b²

3ab(3b+2a)

ab(9b+6a)

b(9ab+6a²)

9ab²+6a²b

3ab(2b+3a)

ab(6b+9a)

b(6ab+9a²)

6ab²+9a²b

3a²b²(2b+3a)

a²b²(6b+9a)

b²(6a²b+9a³)

6a²b³+9a³b²

Now that we have all expressions fully simplified, let's compare to see which one matches.

Our first expression is nowhere close to what our original expression is, 1 is incorrect.

Our second expression is close, but it has the 9 and the 6 flipped, even if we rearrange the expression like this, 6a²b+9ab², it still doesn't match, so 2 is also incorrect.

Our third expression has the correct numbers, variables, placement, and exponents, so 3 is correct.

Our fourth expression has incorrect exponents, the expression made every variable multiplied by ab an extra time, so 4 is incorrect.

In summary, you should pick number 3, because it is equivalent.

I hope this was helpful, keep learning! :D

User Wahid Masud
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3.0k points
15 votes
15 votes

Answer:

C. 3ab ( 2b + 3a )

Explanation:

substitution

User Rhopman
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2.8k points