Question

(a+b)-(a+b(a-b)-a(b+a))

Answer 1

(a+b)-(a+b(a-b)-a(b+a)) = (а + b) - (a + ba - b² - ab - a²) = a + b - a - ab + b² + ab - a² = b + b² - a²

Answer 2

Let's simplify the expression step by step:

First, let's simplify the term inside the parentheses:

a + b(a - b) - a(b + a)

= a + ba - bb - ab - aa = -ab - aa + ba - bb + a = a - a(a + b) - b(a + b) = (a + b)(1 - a - b)

Now, we can substitute this result back into the original expression:

(a + b) - (a + b)(1 - a - b)

= (a + b) - a - b + (a + b)(a + b - 1) = -a^2 - b^2 + 2ab + a + b

Therefore, the final simplified expression is:

-a^2 - b^2 + 2ab + a + b