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

Question

Joey Erin
(2x−5)(x+12)

(2x)(x)+(2x)(12)+(−5)(x)+(−5)(12)

2x+24x−5x−60

21x−60

(2x−5)(x+12)

(2x)(x)+(2x)(12)+(−5)(x)+(−5)(12)

2x2+24x−5x−60

2x2+19x−60

Which classmate completed the problem correctly? (1 point)

Explain what mistake the other classmate made. Use complete sentences

Answer 1

Erin completed the problem correctly. She correctly expanded the binomials and combined like terms to arrive at the final answer, \(2x^2 + 19x - 60\).

Joey, on the other hand, made a mistake in combining the like terms. His intermediate step correctly showed the four products: \(2x^2\), \(24x\), \(-5x\), and \(-60\). However, when combining the like terms \(24x\) and \(-5x\), he incorrectly calculated the result as \(21x\) instead of the correct sum of \(19x\). Thus, his final answer was incorrect because he failed to accurately combine those coefficients.