Math Problem Statement
Factorise a to to the power 3 b minus AP to the power 3 using middle term splitting solve
Solution
Let's factorize the expression using the middle term splitting method. The expression is:
Step 1: Factor out the common terms
We can see that both terms have a common factor of . Let's factor it out first:
Step 2: Apply the difference of squares
Now, we are left with the expression , which is a difference of squares. We can factor it as:
Step 3: Write the final factorized form
Substitute the factorization of back into the expression:
Thus, the fully factorized form of is:
Would you like further details on any of these steps or have any specific questions?
Here are 5 related questions:
- How would you factor other cubic expressions, like ?
- Can you apply the middle term splitting method to polynomials of higher degrees?
- What is the difference of squares, and how can it be used in other factorizations?
- How do you recognize common factors in complex algebraic expressions?
- 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.
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Math Problem Analysis
Mathematical Concepts
Algebra
Factorization
Difference of Squares
Formulas
a^3b - ab^3 = ab(a^2 - b^2)
a^2 - b^2 = (a - b)(a + b)
Theorems
Difference of Squares Theorem
Suitable Grade Level
Grades 9-10