Question

(2ab+b)^2-(a-2b)(a+2b)-4ab упростить

Answer 1

4a^2b^2 + 4ab^2 + 5b^2 - a^2 -4ab

Answer 2

To simplify the expression (2ab+b)^2 - (a-2b)(a+2b) - 4ab, let's follow these steps:

Step 1: Expand the squares: (2ab + b)^2 = (2ab + b)(2ab + b) = 4a^2b^2 + 2ab^2 + 2ab^2 + b^2 = 4a^2b^2 + 4ab^2 + b^2.

Step 2: Expand the multiplication (a-2b)(a+2b): (a-2b)(a+2b) = a(a) + a(2b) - 2b(a) - 2b(2b) = a^2 + 2ab - 2ab - 4b^2 = a^2 - 4b^2.

Now, let's rewrite the original expression with the expanded terms:

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

Step 3: Remove the parentheses and combine like terms: = 4a^2b^2 + 4ab^2 + b^2 - a^2 + 4b^2 - 4ab = 4a^2b^2 - a^2 + 4ab^2 + 4b^2 - 4ab

Step 4: Combine similar terms: = 4a^2b^2 - a^2 + 4b^2(1 - a) - 4ab = 4a^2b^2 - a^2 + 4b^2 - 4ab

So, the simplified expression is: 4a^2b^2 - a^2 + 4b^2 - 4ab