Factorise a to to the power 3 b minus AP to the power 3 using middle term splitting solve

Let's factorize the expression \( a^3b - ab^3 \) using the middle term splitting method. The expression is:

\[
a^3b - ab^3
\]

### Step 1: Factor out the common terms
We can see that both terms have a common factor of \( ab \). Let's factor it out first:

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

### Step 2: Apply the difference of squares
Now, we are left with the expression \( a^2 - b^2 \), which is a difference of squares. We can factor it as:

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

### Step 3: Write the final factorized form
Substitute the factorization of \( a^2 - b^2 \) back into the expression:

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

Thus, the fully factorized form of \( a^3b - ab^3 \) is:

\[
ab(a - b)(a + b)
\]

Would you like further details on any of these steps or have any specific questions?

Here are 5 related questions:
1. How would you factor other cubic expressions, like \( a^3 - b^3 \)?
2. Can you apply the middle term splitting method to polynomials of higher degrees?
3. What is the difference of squares, and how can it be used in other factorizations?
4. How do you recognize common factors in complex algebraic expressions?
5. What are other factorization techniques besides middle term splitting?

**Tip**: Always look for common factors first when attempting to factor any expression—it simplifies the process significantly.

Factorise a to the power 3 b minus ab to the power 3 using middle term splitting.

Learn how to factorize the expression a^3b - ab^3 using the middle term splitting method. This problem explores algebraic concepts such as factorization and the difference of squares, suitable for students in Grades 9-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation