https://file.aiquickdraw.com/mathbot/file/1725496680083t18bpqqz.jpg

The equation shown in the image is:

\[
216p^3 + 125q^3
\]

This is a sum of cubes, which can be factored using the formula:

\[
a^3 + b^3 = (a + b)(a^2 - ab + b^2)
\]

In this case, we can rewrite \(216p^3\) and \(125q^3\) as perfect cubes:

\[
216p^3 = (6p)^3 \quad \text{and} \quad 125q^3 = (5q)^3
\]

Now, apply the sum of cubes formula:

\[
216p^3 + 125q^3 = (6p + 5q)\left((6p)^2 - (6p)(5q) + (5q)^2\right)
\]

Simplifying the second part:

\[
= (6p + 5q)\left(36p^2 - 30pq + 25q^2\right)
\]

So the factored form is:

\[
216p^3 + 125q^3 = (6p + 5q)(36p^2 - 30pq + 25q^2)
\]

Let me know if you'd like further explanation or details on any step!

Here are 5 related questions for practice:
1. How do you factor the difference of cubes, like \(a^3 - b^3\)?
2. What is the formula for the cube of a binomial, like \((x + y)^3\)?
3. How would you factor \(27x^3 + 64y^3\)?
4. Can you solve for roots in a quadratic equation like \(36p^2 - 30pq + 25q^2 = 0\)?
5. What happens if we try to factor \(p^3 + q^3\)?

**Tip**: Recognizing common algebraic identities like the sum and difference of cubes can make factoring polynomials easier!

Learn how to factor the sum of cubes expression 216p^3 + 125q^3 using the formula for factoring cubes. This problem demonstrates key algebraic concepts such as cubic expressions and factoring techniques, suitable for high school students.

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