Question

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)

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 made a mistake in his calculation. His final answer of \( 21x - 60 \) is incorrect because he failed to correctly combine the coefficients of the \( x \) terms.

In Erin's work, she correctly calculated the individual products:

- \( (2x)(x) = 2x^2 \)
- \( (2x)(12) = 24x \)
- \( (-5)(x) = -5x \)
- \( (-5)(12) = -60 \)

She then properly combined the like terms for the \( x \) coefficients:

\[ 24x - 5x = 19x \]

Thus, her final answer is \( 2x^2 + 19x - 60 \), which is correct.

Joey's mistake was in the addition of the coefficients. He mistakenly summed \( 24x - 5x \) as \( 21x \) instead of \( 19x \). This resulted in an incorrect final polynomial, leading him to arrive at an incorrect answer.