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? Explain what mistake the other classmate made. Use complete sentences to receive credit.

Answer 1

Erin completed the problem correctly. She accurately expanded the binomials and combined like terms. Her calculation shows:

1. \( (2x)(x) = 2x^2 \)
2. \( (2x)(12) = 24x \)
3. \( (-5)(x) = -5x \)
4. \( (-5)(12) = -60 \)

When combining the like terms \( 24x \) and \( -5x \), she correctly calculated \( 24x - 5x = 19x \). Thus, the final result is \( 2x^2 + 19x - 60 \).

On the other hand, Joey made a mistake in combining the terms after expansion. He started correctly with:

1. \( (2x)(x) = 2x^2 \)
2. \( (2x)(12) = 24x \)
3. \( (-5)(x) = -5x \)
4. \( (-5)(12) = -60 \)

However, when he combined the like terms \( 24x \) and \( -5x \), he incorrectly computed them as \( 21x \) instead of \( 19x \). Therefore, his final result of \( 21x - 60 \) is incorrect because he failed to correctly add the coefficients of the \( x \) terms. As a result, he had the wrong coefficient for the \( x \) term in his final answer.