Question

Two classmates are working on multiplying the binomials (2x-5)(x+12). Their work is below:

Joey's Work:
(2x - 5) (x + 12)
(2x) (x) + (2x) (12) + (-5) (x) + (-5) (12)
2x + 24x - 5x - 60
21x - 60

Erin's Work:
(2x - 5) (x + 12)
(2x) (x) + (2x) (12) +
2x^2 + 24x - 5x - 60
2x^2 + 19x - 60

Which classmate completed the problem correctly? Explain what mistake the other classmate made.

Answer 1

To determine which classmate completed the multiplication of the binomials correctly, let's first review their work and then calculate the product of the binomials \((2x-5)(x+12)\) step by step.

### Joey's Work:
1. Joey wrote:
\[
(2x - 5)(x + 12)
\]
2. He multiplied out the terms:
\[
(2x)(x) + (2x)(12) + (-5)(x) + (-5)(12)
\]
This results in:
\[
2x^2 + 24x - 5x - 60
\]
3. Next, he combined the like terms:
\[
2x^2 + (24x - 5x) - 60 = 2x^2 + 19x - 60
\]
Note that Joey incorrectly wrote \(21x\) instead of \(19x\) when combining terms.

### Erin's Work:
1. Erin wrote:
\[
(2x - 5)(x + 12)
\]
2. She also multiplied out the terms correctly:
\[
(2x)(x) + (2x)(12) + (-5)(x) + (-5)(12)
\]
Which gives:
\[
2x^2 + 24x - 5x - 60
\]
3. Erin correctly combined the terms:
\[
2x^2 + (24x - 5x) - 60 = 2x^2 + 19x - 60
\]

### Conclusion:
Erin completed the problem correctly:
\[
2x^2 + 19x - 60
\]

Joey made a mistake when combining the coefficients of \(x\). He mistakenly wrote \(21x\) instead of \(19x\), which led to an incorrect final expression. Thus, Erin is correct, and Joey made a simplification error in combining the terms.