(a + b)(c - d) = ac - ad + bc - bd
Let's apply this formula to the given expression:
(√3 + √7)(2√3 - √7)
First, let's multiply the terms inside the parentheses:
√3 * 2√3 = 2√9 = 2√(33) = 2 * 3 = 6 √3 * -√7 = -√(37) = -√21 √7 * 2√3 = 2√(73) = 2√21 √7 * -√7 = -√(77) = -√49 = -7
Now, let's combine the terms:
6 - √21 + 2√21 - 7
Next, simplify the terms:
6 - 7 + √21(2 - 1)
Combine the integers:
-1 + √21(1)
Finally, simplify the expression:
-1 + √21
