Question

(2a+b)в квадрате-(a-2b)в квадрате

Answer 1

(2a+b)2-(a-2b)2 =4a2+4ab+b2-a2+4ab-4b2=
= (a+3b)(3a-b) = 3a2 + 8ab - 3b2

Answer 2

To simplify the expression, let's expand both terms and then combine like terms:

1. Expand (2a + b)²: (2a + b)² = (2a + b) * (2a + b) = 2a * (2a) + 2a * b + b * (2a) + b * b = 4a² + 2ab + 2ab + b² = 4a² + 4ab + b²

2. Expand (a - 2b)²: (a - 2b)² = (a - 2b) * (a - 2b) = a * a + a * (-2b) + (-2b) * a + (-2b) * (-2b) = a² - 2ab - 2ab + 4b² = a² - 4ab + 4b²

Now, let's subtract the second expression from the first:

(2a + b)² - (a - 2b)² = (4a² + 4ab + b²) - (a² - 4ab + 4b²)

Now, distribute the negative sign to the terms inside the parentheses:

= 4a² + 4ab + b² - a² + 4ab - 4b²

Finally, combine like terms:

= (4a² - a²) + (4ab + 4ab) + (b² - 4b²) = 3a² + 8ab - 3b²

So, the simplified expression is 3a² + 8ab - 3b².