Theory question 101
Binary OperationsA binary operation Δ is defined on the set of real numbers, R, by a Δ b = a3 − b3. Without using calculator, find the value of (√3 + √2) Δ (√3 − √2), leaving the answer in surd form.
Show the model answer
Model answer
(√3 + √2)³ = 3√3 + 9√2 + 6√3 + 2√2 = 9√3 + 11√2.
(√3 − √2)³ = 9√3 − 11√2.
Difference = 22√2.
Explanation
Expand each cube with the binomial pattern.