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Which of the following demonstrates the Distributive Property?

4(2a + 3) = 8a + 3
4(2a + 3) = 2a + 12
4(2a + 3) = 6a + 7
4(2a + 3) = 8a + 12

1 Answer

5 votes

Answer: D) 4(2a + 3) = 8a + 12

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Step-by-step explanation:

The distributive property is

x(y+z) = x*y + x*z

We multiply the outer term x by each term inside the parenthesis y and z, and add up the results.

In this case, the outer term 4 is multiplied by the terms inside the parenthesis 2a and 3

So,

  • 4 times 2a = 8a
  • 4 times 3 = 12

That's how 4(2a+3) becomes 8a+12 We can then say 4(2a+3) = 8a+12 which is choice D.

Choice A is likely a trick answer because many students often forget to multiply the outer term by each term inside. In other words, they would do this mistake

4(2a+3) = 4*2a+3 = 8a+3

but we would need to multiply that 3 by 4 as well

Choice B seems to be a similar idea, but the 2a is left out this time.

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Extra info (optional section)

The 4 outside the (2a+3) means we have four copies of (2a+3) being added together. Recall that multiplication is effectively repeated addition.

So we could say

4(2a+3) = (2a+3)+(2a+3)+(2a+3)+(2a+3)

4(2a+3) = (2a+2a+2a+2a) + (3+3+3+3)

4(2a+3) = 4*(2a) + 4*(3)

4(2a+3) = 8a + 12

This is one example showing how the distributive property works.

User Skyp
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