Question

Two of your friends, Matt and Karen, both run to you to settle a dispute. They were working on a math problem, and got different answers. Wisely, you decide to look at their work to see if you can spot the source of confusion.

Matt
6 – 4(3 – 5)2 + 30 ÷ 5
6 – 4(–2)2 + 30 ÷ 5
6 – 4(4) + 30 ÷ 5
6 – 16 + 30 ÷ 5
−10 + 30 ÷ 5
20 ÷ 5
4
Karen
6 – 4(3 – 5)2 + 30 ÷ 5
6 – 4(–2)2 + 30 ÷ 5
6 – 4(−4) + 30 ÷ 5
6 + 16 + 30 ÷ 5
6 + 16 + 6
22 + 6
28
Explain to Matt and Karen who, if either, is correct, and identify error

Answer 1

(-2)^2 = +4

Answer 2

dude, please when dealing with exponents don't do things like
6 – 4(3 – 5)2 + 30 ÷ 5
either do 6 – 4(3 – 5)^2 + 30 ÷ 5 or 6 – 4(3 – 5)² + 30 ÷ 5

Answer 3

They both made mistakes, so both of their answers are wrong.

Answer 4

Matt
\(6 – 4(3 – 5)^2 + 30 ÷ 5 \)
\(= 6 – 4(–2)^2 + 30 ÷ 5 \)
\(=6 – 4(4) + 30 ÷ 5 \)
\(=6 – 16 + 30 ÷ 5 \)
\(=−10 + \color{red}{30 ÷ 5} \)
\(=-10 + \color{red}{6} \)
\(=-4 \)

Karen
\(6 – 4(3 – 5)^2 + 30 ÷ 5 \)
\(=6 – 4\color{red}{(–2)^2} + 30 ÷ 5 \)
\(=6 – 4\color{red}{(4)} + 30 ÷ 5 \)
\(=6 - 16 + 30 ÷ 5 \)
\(=6 - 16 + 6 \)
\(=-10 + 6 \)
\(=-4\)