https://file.aiquickdraw.com/mathbot/file/172589536974382we0fo9.jpg

The equation shown in the image is:

\[
(x + a)^3 = x^3
\]

This equation can be simplified and analyzed by expanding the left-hand side.

### Expanding the left-hand side:
Using the binomial expansion formula for \((x + a)^3\), we get:
\[
(x + a)^3 = x^3 + 3x^2a + 3xa^2 + a^3
\]

Thus, the equation becomes:
\[
x^3 + 3x^2a + 3xa^2 + a^3 = x^3
\]

Now, subtract \(x^3\) from both sides:
\[
3x^2a + 3xa^2 + a^3 = 0
\]

This is the resulting equation after simplifying.

Would you like to explore this equation further or solve for \(a\) or \(x\)? Feel free to ask for more details!

### Related questions:
1. What happens if we solve for \(a\) in this equation?
2. How can this type of equation be used in real-world problems?
3. What would the graph of this equation look like?
4. How can we factor the simplified equation?
5. What methods can be used to solve a cubic equation like this?

### Tip:
When expanding binomials, the binomial theorem can be very helpful, especially for higher powers.

Learn how to solve the cubic equation (x + a)^3 = x^3 by expanding the binomial using the binomial theorem. This problem covers key algebraic concepts such as binomial expansion and simplifying cubic equations. Suitable for students in Grades 9-12.

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