Math Problem Statement
Expand and simplify the expression (3a − 2b)(6a − b) + 4a(9a + 4b).
Solution
Let's expand and simplify the expression:
Step 1: Expand each part of the expression.
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Expand using the distributive property: Combine the like terms:
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Expand :
Step 2: Combine the expanded parts.
Combine like terms:
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For terms:
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For terms: -15ab + 16ab = 1ab \quad \text{(or simply ab)}
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For terms:
Final Simplified Expression:
This is the expanded and simplified form of the given expression.
Would you like more details or have any questions about this process?
Here are 5 related questions you might find interesting:
- How would the expansion change if the sign of were reversed in the original expression?
- What would happen if the coefficients of and were doubled in the original expression?
- How do you factor the expression ?
- What is the geometric interpretation of the simplified expression?
- How would the solution change if the powers of and were different in the original expression?
Tip: When expanding and simplifying expressions, it helps to carefully track each term to avoid mistakes in combining like terms.
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Math Problem Analysis
Mathematical Concepts
Algebra
Distributive Property
Combining Like Terms
Formulas
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Theorems
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Suitable Grade Level
Grades 9-12