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