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

Question

Joey
(2x−5)(x+12)

(2x)(x)+(2x)(12)+(−5)(x)+(−5)(12)

2x+24x−5x−60

21x−60

erin

(2x−5)(x+12)

(2x)(x)+(2x)(12)+(−5)(x)+(−5)(12)

2x^2+24x−5x−60

2x^2+19x−60

Which classmate completed the problem correctly? (1 point)

Explain what mistake the other classmate made. Use complete sentences to receive credit. (2 points)

(3 points)

Answer 1

Joey did not complete the problem correctly. His error occurred during the simplification step where he combined the terms.

Here's what he wrote:

1. He started with the correct expression: \( (2x)(x) + (2x)(12) + (-5)(x) + (-5)(12) \), which expands and gives: \[ 2x^2 + 24x - 5x - 60 \]

2. Next, when combining the like terms \( 24x \) and \( -5x \), Joey should have calculated: \[ 24x - 5x = 19x \] However, he mistakenly wrote \( 21x \) instead of \( 19x \).

3. Thus, Joey’s final expression of \( 21x - 60 \) is incorrect.

Erin completed the problem correctly. She properly tracked the initial terms and correctly combined \( 24x - 5x \) to get \( 19x \). Her final expression \( 2x^2 + 19x - 60 \) is the correct product of the binomials.

In summary, Joey's mistake was in the addition of the coefficients of the \( x \) terms, where he wrote \( 21x \) instead of the correct \( 19x \).