The equation you've written is:

\[
(x + a)(x + b) = (x + a)x + (x + a)b
\]

Let's simplify and compare both sides of the equation.

### Step 1: Expanding the Left Side
Expand \((x + a)(x + b)\):

\[
(x + a)(x + b) = x \cdot x + x \cdot b + a \cdot x + a \cdot b = x^2 + bx + ax + ab = x^2 + (a + b)x + ab
\]

### Step 2: Expanding the Right Side
Expand the right side \((x + a)x + (x + a)b\):

1. Expand \((x + a)x\):

   \[
   (x + a)x = x \cdot x + a \cdot x = x^2 + ax
   \]

2. Expand \((x + a)b\):

   \[
   (x + a)b = x \cdot b + a \cdot b = bx + ab
   \]

3. Combine the terms:

   \[
   (x + a)x + (x + a)b = x^2 + ax + bx + ab = x^2 + (a + b)x + ab
   \]

### Conclusion
Both sides simplify to the same expression:

\[
x^2 + (a + b)x + ab
\]

Therefore, the equation is valid.

Would you like further details, or do you have any questions? 

Here are some related questions you might find helpful:

1. What are common mistakes when expanding binomials?
2. How do you simplify expressions involving polynomials?
3. What is the distributive property and how does it apply here?
4. Can this technique be applied to polynomials with more than two terms?
5. How does this relate to factoring quadratic expressions?

**Tip:** When expanding expressions, always distribute each term in the first parenthesis by each term in the second parenthesis to avoid missing terms!

Discover how to expand binomials like (x + a)(x + b) using the distributive property. This detailed solution simplifies the expression to x^2 + (a + b)x + ab, explaining each step. Suitable for students in Grades 8-10.

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