Let's go through the problems shown in the image one by one.

Question 38:

$0 + x + y = x + y$

This equation simplifies directly, as adding zero to any number doesn't change its value. Therefore: $0 + x + y = x + y$ This is true, so the correct answer is True.

Question 39:

$xy + x = 2xy$

We can factor the left side: $xy + x = x(y + 1)$ So the equation becomes: $x(y + 1) = 2xy$ If we divide both sides by $x$ (assuming $x \neq 0$): $y + 1 = 2y$ Now, subtract $y$ from both sides: $1 = y$ This equation holds true when $y = 1$. Since it only holds for this specific value of $y$, the equation is Not True in general.

Question 40:

$x^2 - xy = 2y^2$

This equation doesn't simplify nicely, so we'd need to test it for specific values of $x$ and $y$. For now, this equation is Not True unless proven otherwise for specific values of $x$ and $y$.

Would you like further clarification or details on any of these problems?

Related Questions:

1. What would happen if $y = 0$ in Question 39? How would that affect the equation?
2. Can you factor the expression in Question 40 further?
3. What are some possible values of $x$ and $y$ that would satisfy Question 40?
4. If $x = 1$, does the equation in Question 39 still hold true?
5. What is the general process of verifying whether an equation is true for all values of variables?

Tip:

When dealing with algebraic equations, factoring can often simplify the problem and make it easier to verify whether the equation holds for all values or just specific ones.