Math Problem Statement
Solution
The given expression to simplify and factor is:
Step 1: Expand the terms
Expand both parts separately:
-
First term: Using distributive property: Expanding further: and So:
-
Second term: Expanding : So:
Step 2: Combine the expressions
Now, substitute back the expanded terms into the original expression: Combine like terms:
- cancels out:
- cancels out:
- Combine
- The remaining terms:
So, the simplified expression is:
Step 3: Factor the expression
Now factor the simplified expression:
Conclusion:
The correct answer is:
Would you like more details or have any further questions?
Related Questions:
- How do you factor quadratic expressions like ?
- What are the steps to expand binomial expressions?
- How do you recognize common factoring patterns in expressions?
- What is the distributive property and how is it used in algebra?
- How can you solve similar factorization problems with three variables?
Tip:
Always double-check by re-expanding your factored terms to verify they match the original expression.
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Math Problem Analysis
Mathematical Concepts
Algebra
Factoring
Simplifying Expressions
Quadratic Expansions
Formulas
Distributive property: (a + b)(c + d) = ac + ad + bc + bd
(a - b)^2 = a^2 - 2ab + b^2
Theorems
Distributive Property
Factoring and Expanding Binomials
Suitable Grade Level
Grades 9-11