To determine which classmate completed the multiplication of the binomials correctly, let's first review their work and then calculate the product of the binomials \((2x-5)(x+12)\) step by step.
Joey's Work:
- Joey wrote: \[ (2x - 5)(x + 12) \]
- He multiplied out the terms: \[ (2x)(x) + (2x)(12) + (-5)(x) + (-5)(12) \] This results in: \[ 2x^2 + 24x - 5x - 60 \]
- Next, he combined the like terms: \[ 2x^2 + (24x - 5x) - 60 = 2x^2 + 19x - 60 \] Note that Joey incorrectly wrote \(21x\) instead of \(19x\) when combining terms.
Erin's Work:
- Erin wrote: \[ (2x - 5)(x + 12) \]
- She also multiplied out the terms correctly: \[ (2x)(x) + (2x)(12) + (-5)(x) + (-5)(12) \] Which gives: \[ 2x^2 + 24x - 5x - 60 \]
- Erin correctly combined the terms: \[ 2x^2 + (24x - 5x) - 60 = 2x^2 + 19x - 60 \]
Conclusion:
Erin completed the problem correctly: \[ 2x^2 + 19x - 60 \]
Joey made a mistake when combining the coefficients of \(x\). He mistakenly wrote \(21x\) instead of \(19x\), which led to an incorrect final expression. Thus, Erin is correct, and Joey made a simplification error in combining the terms.
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