Two classmates are working on multiplying the binomials (2x-5)(x+12). Their work is below: 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 to receive credit. (2 points) (3 points)

Answer 1

Joey completed the problem correctly. His final expression is \(2x^2 + 19x - 60\).

Erin, on the other hand, made a mistake in combining the like terms in the expression \(2x + 24x - 5x\). Joey correctly simplified this to \(21x\), while Erin incorrectly stated that this resulted in \(19x\). Therefore, Erin's final result is incorrect because she miscalculated the coefficient of \(x\) after combining the terms.

In summary, Joey's work accurately combined the terms to yield the correct coefficient of \(x\), while Erin's oversight led to an error in her final expression.