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. (2 points)

(3 points)

Answer 1

Joey made a mistake in his final expression, while Erin completed the problem correctly.

Joey's Work:

1. Joey starts correctly: (2x)(x) + (2x)(12) + (-5)(x) + (-5)(12).
2. He correctly calculates these as: 2x^2 + 24x - 5x - 60.
3. However, in his final step, he incorrectly simplifies 24x - 5x to 21x instead of correctly calculating it to 19x.

Erin's Work:

1. Erin also starts with the correct expansion: (2x)(x) + (2x)(12) + (-5)(x) + (-5)(12).
2. She correctly simplifies it to: 2x^2 + 24x - 5x - 60.
3. She accurately combines like terms: 24x - 5x equals 19x, resulting in 2x^2 + 19x - 60.

Conclusion:

• Joey's mistake was in the final simplification step where he miscalculated the coefficient of x by incorrectly writing 24x - 5x as 21x instead of 19x.
• Erin's final expression is correct with the binomial multiplication resulting in 2x^2 + 19x - 60.