Question

(2√а + 3√b)² + (2√a + 3√b)(2√a - 3√b)​

Answer 1

Ответ:

8a + 12√(ab).

Пошаговое объяснение:

(2√а + 3√b)² + (2√a + 3√b)(2√a - 3√b)​ = (2√а)² + 2•2√а•3√b + (3√b)² + (2√а)² - (3√b)² = 4a + 12√(ab) + 4a = 8a + 12√(ab).

Answer 2

To simplify the expression, let's break it down step by step.

First, let's expand the first term, which is (2√a + 3√b)²: (2√a + 3√b)² = (2√a + 3√b)(2√a + 3√b)

Using the distributive property, we can multiply each term: = (2√a)(2√a) + (2√a)(3√b) + (3√b)(2√a) + (3√b)(3√b) = 4a + 6√ab + 6√ab + 9b = 4a + 12√ab + 9b

Next, let's expand the second term, which is (2√a + 3√b)(2√a - 3√b): = (2√a)(2√a) + (2√a)(-3√b) + (3√b)(2√a) + (3√b)(-3√b) = 4a - 6√ab + 6√ab - 9b = 4a - 9b

Now, let's combine the two terms: (2√a + 3√b)² + (2√a + 3√b)(2√a - 3√b) = (4a + 12√ab + 9b) + (4a - 9b) = 4a + 12√ab + 9b + 4a - 9b = 8a + 12√ab

So the simplified expression is 8a + 12√ab.