Question

Which of the following is the lowest?

• A. \(30^2 - 12^2 - 3^2\)
• B. \(35^2 - 14^2 - 6^2\)
• C. \(30^2 - 10^2 - 5^3\)
• D. \(33^2 - 17^2 - 1^2\)

Hint:

Work out each expression fully before comparing; option (3) has a cube in its last term, not a square, so do not skip that detail.

Answer 1

The Correct Option is C

Step 1: Work out option (1).
\[ 30^2 - 12^2 - 3^2 = 900 - 144 - 9 = 747 \]

Step 2: Work out option (2).
\[ 35^2 - 14^2 - 6^2 = 1225 - 196 - 36 = 993 \]

Step 3: Work out option (3), watching the exponent carefully.
This one has a cube in the last term, not a square:
\[ 30^2 - 10^2 - 5^3 = 900 - 100 - 125 = 675 \]

Step 4: Work out option (4).
\[ 33^2 - 17^2 - 1^2 = 1089 - 289 - 1 = 799 \]

Step 5: Compare all four values.
The four results are 747, 993, 675 and 799. The smallest of these is 675, which comes from option (3).

Final Answer:
Option (3) gives the lowest value.
\[ \boxed{675} \]