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Simplifying Algebraic Expressions: (7x)(2xy)
This article will guide you through simplifying the algebraic expression (7x)(2xy).
Understanding the Basics
Before diving into the simplification, let's recall some fundamental concepts:
- Coefficients: These are numerical values that multiply variables. In our expression, we have 7 and 2.
- Variables: These are letters that represent unknown values. Here, we have x and y.
- Exponents: These indicate how many times a variable is multiplied by itself.
Simplifying the Expression
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Commutative Property: We can rearrange the terms within multiplication without affecting the result. So, we can rewrite the expression as: 7 * 2 * x * x * y.
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Multiplication of Coefficients: Multiply the numerical coefficients together: 7 * 2 = 14.
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Multiplication of Variables: Multiply the variables with the same base by adding their exponents: x * x = x².
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Combining Results: Putting it all together, we get: 14x²y.
Final Result
Therefore, the simplified form of (7x)(2xy) is 14x²y.
Key Takeaways
- Simplifying algebraic expressions involves combining like terms and applying the basic rules of arithmetic.
- Understanding the commutative property and the rules for multiplying variables with exponents is crucial.
- Remember to always combine coefficients and variables with the same base.