Question

two friends, kevin and sophie, are evaluating the expression (-4) × (4 + 5) using the distributive property, as shown below: kevin: (-16) + (-4) × 5 sophie: (-4) × 4 + 20 who evaluated the expression correctly? a neither kevin nor sophie b kevin c both kevin and sophie d sophie

Explanation:

Step1: Recall distributive property

The distributive property is $a\times(b+c) = a\times b + a\times c$. For this problem $a=-4$, $b=4$, $c=5$.

Step2: Evaluate Kevin's work

Kevin writes $(-16) + (-4)\times5$. First calculate $(-4)\times4=-16$, so his expansion is correct. Now compute the full value: $(-16) + (-20) = -36$.

Step3: Evaluate Sophie's work

Sophie writes $(-4)\times4 +20$. $(-4)\times5=-20$, not $20$, so her expansion is wrong. Her calculation gives $-16+20=4$, which is incorrect.

Step4: Verify direct calculation

Directly compute $(-4)\times(4+5)=(-4)\times9=-36$, matching Kevin's result.

Answer:

B. Kevin