Question

(2a+b)^2-(2a-3b)(3b+2a)

Answer 1

(2a + b)² - (2a - 3b)(3b + 2a) = 4a² + 4ab + b² - (2a - 3b)(2a + 3b) = 4a² + 4ab + b² - 4a² + 9b² = 4ab + 10b²
Ответ: 10b² + 4ab

Answer 2

Let's simplify the given expression step by step:

(2a + b)^2 - (2a - 3b)(3b + 2a)

Step 1: Expand the square of the first term (2a + b)^2

(2a + b)^2 = (2a + b)(2a + b) = 4a^2 + 2ab + 2ab + b^2 = 4a^2 + 4ab + b^2

Step 2: Expand the second term (2a - 3b)(3b + 2a)

(2a - 3b)(3b + 2a) = 2a * 3b + 2a * 2a - 3b * 3b - 3b * 2a = 6ab + 4a^2 - 9b^2 - 6ab = 4a^2 - 9b^2

Step 3: Substitute the results from Step 1 and Step 2 back into the original expression:

(2a + b)^2 - (2a - 3b)(3b + 2a) = (4a^2 + 4ab + b^2) - (4a^2 - 9b^2)

Step 4: Distribute the negative sign to both terms in the second parentheses:

(4a^2 + 4ab + b^2) - (4a^2 - 9b^2) = 4a^2 + 4ab + b^2 - 4a^2 + 9b^2

Step 5: Combine like terms:

4a^2 - 4a^2 = 0 (the squared terms cancel out) 4ab + b^2 - 9b^2 = 4ab - 8b^2

So, the simplified expression is:

4ab - 8b^2