The expression \((q - r)^3\) represents the cube of the binomial \(q - r\). To expand this expression, you can apply the binomial theorem or use the formula for the cube of a binomial:

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

Substituting \(a = q\) and \(b = r\):

\[
(q - r)^3 = q^3 - 3q^2r + 3qr^2 - r^3
\]

So, the expanded form of \((q - r)^3\) is:

\[
q^3 - 3q^2r + 3qr^2 - r^3
\]

Would you like more details on how to apply the binomial theorem for this expansion, or do you have any questions?

Here are 5 related questions to explore further:
1. How would you expand \((q + r)^3\) using the binomial theorem?
2. What is the expansion of \((2q - 3r)^3\)?
3. How can you factor the expression \(q^3 - r^3\)?
4. What is the general form of \((a - b)^n\) using the binomial theorem?
5. How does the expansion change if the exponents in \((q - r)^3\) were higher, like \((q - r)^4\)?

**Tip:** When expanding binomials, understanding the binomial coefficients and how they relate to Pascal's triangle can make the process quicker and more intuitive.

Learn how to expand the expression (q - r)^3 using the binomial theorem. Detailed step-by-step explanation with the cube of a binomial formula. Suitable for high school and beyond.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation