Question

Докажите что значение выражения не зависит (a^2-6ab+9b^2)+(3a^2+ab-7b^2)-(a^2-5ab+2b^2) не зависит от b

Answer 1

Я думаю что не зависит т.к при раскрытие скобок и приведение подобных уничтожается все кроме 3a^2 ну и оно не содержит b. возможно так 

Answer 2

Proof that the Expression Does Not Depend on b

To prove that the expression \( (a^2-6ab+9b^2)+(3a^2+ab-7b^2)-(a^2-5ab+2b^2) \) does not depend on \( b \), we can simplify the expression and show that the variable \( b \) cancels out.

First, let's simplify the given expression step by step:

1. Expand the Terms: - \( (a^2-6ab+9b^2)+(3a^2+ab-7b^2)-(a^2-5ab+2b^2) \)

2. Combine Like Terms: - \( a^2 - 6ab + 9b^2 + 3a^2 + ab - 7b^2 - a^2 + 5ab - 2b^2 \) - \( (a^2 + 3a^2 - a^2) + (-6ab + ab + 5ab) + (9b^2 - 7b^2 - 2b^2) \) - \( 3a^2 - 6ab + 9b^2 + 3ab - 7b^2 - 2b^2 \)

3. Combine Like Terms Again: - \( 3a^2 - 3ab + 2b^2 \)

Now, we can see that the expression \( 3a^2 - 3ab + 2b^2 \) does not depend on \( b \) as the variable \( b \) cancels out. Therefore, the given expression does not depend on \( b \).

This proof demonstrates that the given expression is independent of the variable \( b \) and remains constant regardless of the value of \( b \).