https://file.aiquickdraw.com/mathbot/file/1729439045751gnu8e5w5.jpg

The expression in the image is \( 64 - 27w^3 \), and it asks to factor it.

This is a difference of cubes, as it follows the form \( a^3 - b^3 \), where:

\[
64 = 4^3 \quad \text{and} \quad 27w^3 = (3w)^3
\]

The general factorization of a difference of cubes is:

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

Using this formula, we substitute \( a = 4 \) and \( b = 3w \):

\[
64 - 27w^3 = (4 - 3w)(4^2 + 4 \cdot 3w + (3w)^2)
\]

Simplifying the second factor:

\[
4^2 + 4 \cdot 3w + (3w)^2 = 16 + 12w + 9w^2
\]

Thus, the factored form of \( 64 - 27w^3 \) is:

\[
(4 - 3w)(16 + 12w + 9w^2)
\]

Would you like more details or further explanation?

Here are 5 related questions for practice:
1. How would you factor the expression \( 125 - 8w^3 \)?
2. What is the general formula for factoring a sum of cubes?
3. Can you factor \( 64x^3 - 27y^3 \) using a similar method?
4. How would you expand the expression \( (4 - 3w)(16 + 12w + 9w^2) \)?
5. What other types of polynomial factorizations are similar to the difference of cubes?

**Tip:** Recognizing patterns like the difference of cubes helps you quickly apply the appropriate formulas for factorization.

Learn how to factor the expression 64 - 27w^3 using the difference of cubes method. This detailed guide covers key algebraic concepts and formulas, making it suitable for students in Grades 9-12.

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