Question

(2x-y)(2x+y) - (2x - y)^2 + 2y^2

Answer 1

Смотри..........................

Answer 2

Let's simplify the given expression step by step:

Expression: (2x - y)(2x + y) - (2x - y)^2 + 2y^2

Step 1: Expand the first term using the distributive property: (2x - y)(2x + y) = 4x^2 - xy + 2xy - y^2

Simplified expression: 4x^2 + xy - y^2

Step 2: Expand the second term using the formula (a - b)^2 = a^2 - 2ab + b^2: (2x - y)^2 = (2x)^2 - 2(2x)(-y) + (-y)^2 = 4x^2 + 4xy + y^2

Simplified expression: 4x^2 + 4xy + y^2

Step 3: Add the third term: 2y^2

Final simplified expression: (4x^2 + xy - y^2) - (4x^2 + 4xy + y^2) + 2y^2

Step 4: Combine like terms: 4x^2 - 4x^2 + xy - 4xy - y^2 - y^2 + 2y^2

Simplified expression: -3xy - y^2 + 2y^2

Final simplified expression: -3xy + y^2

Therefore, the simplified expression is -3xy + y^2.