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Expanding the Expression (3m+5)(2m+3)
This article will explore the process of expanding the expression (3m + 5)(2m + 3). This involves applying the distributive property, a fundamental concept in algebra.
Understanding the Distributive Property
The distributive property states that multiplying a sum by a number is the same as multiplying each addend separately by the number and then adding the products. In simpler terms, it allows us to "distribute" the multiplication.
Expanding the Expression
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Identify the terms: We have two binomials: (3m + 5) and (2m + 3).
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Apply the distributive property: We need to multiply each term in the first binomial by each term in the second binomial.
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First term of the first binomial (3m) multiplied by the second binomial: 3m * (2m + 3) = 6m² + 9m
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Second term of the first binomial (5) multiplied by the second binomial: 5 * (2m + 3) = 10m + 15
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Combine the results: Now we add the two products we obtained: 6m² + 9m + 10m + 15
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Simplify by combining like terms: 6m² + 19m + 15
The Final Result
Therefore, the expanded form of (3m + 5)(2m + 3) is 6m² + 19m + 15.
Importance of Expanding Expressions
Expanding expressions is a crucial skill in algebra. It allows us to:
- Simplify expressions: Make them easier to work with.
- Solve equations: By rearranging terms and isolating variables.
- Factorize expressions: Break down expressions into simpler components.
By understanding the distributive property and applying it correctly, we can confidently expand and manipulate algebraic expressions.