Question

(а+в)(а-в)+(а+в)2-а(а+2ав) сделайте сокращённого умножения

Answer 1

А^2-ав+ав-в^2+2а+2в-а^2-2ва^2=-в^2+2а+2в-2ва^2

Answer 2

Simplifying the Expression

To simplify the expression (a + b)(a - b) + (a + b)^2 - a(a + 2ab), we can follow the order of operations and apply the distributive property where necessary.

Let's break down the expression step by step:

1. (a + b)(a - b): - Applying the distributive property, we get a(a - b) + b(a - b). - Simplifying further, we have a^2 - ab + ab - b^2. - The terms -ab + ab cancel each other out, so we are left with a^2 - b^2.

2. (a + b)^2: - Expanding the square, we get (a + b)(a + b). - Applying the distributive property, we have a(a + b) + b(a + b). - Simplifying further, we get a^2 + ab + ab + b^2. - Combining like terms, we have a^2 + 2ab + b^2.

3. a(a + 2ab): - Applying the distributive property, we get a^2 + 2a^2b.

Now, let's put all the simplified terms together:

(a + b)(a - b) + (a + b)^2 - a(a + 2ab) simplifies to (a^2 - b^2) + (a^2 + 2ab + b^2) - (a^2 + 2a^2b).

Simplifying further, we have a^2 - b^2 + a^2 + 2ab + b^2 - a^2 - 2a^2b.

Combining like terms, we get 2ab - 2a^2b.

Therefore, the simplified expression is 2ab - 2a^2b.

Let me know if you need any further assistance!