Question

Students were asked to write an expression equivalent to the expression below:
30a+12b-6a+ 2(9b+c+15)
Their answers are as follows:
36a-30b+2c +30
Ben wrote: 36a - 30b + 2c + 30
Martin:
24a+30b+2c +30
Sara wrote: 24a + 30b + 2c + 15
Martin wrote: 24a + 30b+2c +30
Which, if any, of those students wrote expressions that are equivalent to the original expression?
In the space provided below, either prove why each student's response is equivalent, or explain and correct the student's error.
Sara
| Ben:
Allie wrote: 2(12a + 15b+c+15)
24a+30b+ac+15
Allie:
2(13a +156+c+15)

Answer 1

The equivalent is 24a + 30b +2c + 30

How to determine the equivalent expression

Given the original expression as;

30a+12b-6a+ 2(9b+c+15)

First, expand the bracket, we have

30a + 12b -6a + 18b + 2c + 30

Then, collect like terms

30a -6a + 12b + 18b + 2c + 30

24a + 30b +2c + 30

The equivalent is 24a + 30b +2c + 30

From the result, we have that Martin is correct.

Sara wrote the equivalent as 24a + 30b +2c + 15

She made a mistake in expand the bracket = 2( 9b +c +15) = 18b + 2c + 30

Ben wrote 36a - 30b + 2c + 30. He made a mistake in issuing the sign for 30b = 12b + 18b = +30b

Thus, the equivalent is 24a + 30b +2c + 30

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