Question

A²+ab-5a-5b=a²-b²-a+b=a²-b²+a+b=​

Answer 1

1) a² + ab - 5a - 5b = a(a + b) - 5(a + b) =

= (a + b)(a - 5)

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

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

3) a² - b² + a + b = (a - b)(a + b) + (a + b) =

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

Answer 2

Let's break down each equation step by step:

1. $a^2 + ab - 5a - 5b = a^2 - b^2 - a + b$

First, let's simplify both sides:

$a^2 + ab - 5a - 5b = a^2 - b^2 - a + b$

Subtracting $a^2$ from both sides:

$ab - 5a - 5b = -b^2 - a + b$

Adding $b^2$ and $a$ to both sides:

$ab - 5a - 5b + b^2 + a = - a + b + b^2 + a$

Simplifying further:

$ab - 4a - 4b + b^2 = b^2$

Rearranging terms:

$ab - 4a - 4b = 0$

2. $a^2 - b^2 - a + b = a^2 - b^2 + a + b$

Simplifying both sides:

$a^2 - b^2 - a + b = a^2 - b^2 + a + b$

Canceling out $a^2$ and $b^2$ on both sides:

$-a + b = a + b$

Subtracting $b$ from both sides:

$-a = a$

This equation is not possible for any real values of $a$. It's likely that there was an error in the original statement.

3. $a^2 - b^2 + a + b = a^2 - b^2 + a + b$

This equation is an identity, meaning it is true for all real values of $a$ and $b$.

In summary, the simplified equations are:

1. $ab - 4a - 4b = 0$
2. $a$ cannot be equal to $-a$, so this equation is not possible.
3. $a^2 - b^2 + a + b = a^2 - b^2 + a + b$ is an identity.