Question

two friends, luke and ava, are evaluating the expression ( 7 \times (5 + (-5)) ) using the distributive property, as shown below:
luke: ( 35 + (-5) \times 7 )
ava: ( (5 \times 7) - (-35) )
who evaluated the expression correctly?
a neither luke nor ava
b both luke and ava
c ava
d luke

Explanation:

Step1: Recall distributive property

The distributive property is $a\times(b+c) = a\times b + a\times c$. For $7\times(5 + (-5))$, this expands to $7\times5 + 7\times(-5) = 35 + (-35)$.

Step2: Check Luke's work

Luke's expression is $35 + (-5)\times7 = 35 + (-35)$. This matches the correct expanded form, so Luke is correct.

Step3: Check Ava's work

Ava's expression is $(5\times7) - (-35) = 35 +35$. This does not match the correct expansion, so Ava is incorrect.

Answer:

C. Luke