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?

Answer 1

Let's break down the multiplication of the binomials \((2x - 5)(x + 12)\) step by step.

Using the distributive property (also known as the FOIL method for binomials), we need to multiply each term in the first binomial by each term in the second binomial:

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

Now we combine all these terms together:

\[ 2x^2 + 24x - 5x - 60 \]

Next, we combine the like terms:

\[ 2x^2 + (24x - 5x) - 60 = 2x^2 + 19x - 60 \]

Now, let's compare this to Joey's and Erin's work:

• Joey's final expression: \(21x - 60\) (incorrect)
• Erin's final expression: \(2x^2 + 19x - 60\) (correct)

Thus, Erin completed the problem correctly.