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(3m+1)^2

3 min read Jun 16, 2024
(3m+1)^2

Exploring the Square of (3m + 1)

In mathematics, expanding expressions is a crucial skill. One such expression is the square of (3m + 1). This article will guide you through the process of expanding this expression using the FOIL method and explore its significance.

Expanding the Expression

The FOIL method stands for First, Outer, Inner, Last. This method helps us multiply binomials systematically:

  1. First: Multiply the first terms of each binomial: (3m) * (3m) = 9m²
  2. Outer: Multiply the outer terms of the binomials: (3m) * (1) = 3m
  3. Inner: Multiply the inner terms of the binomials: (1) * (3m) = 3m
  4. Last: Multiply the last terms of each binomial: (1) * (1) = 1

Now, we combine the results: 9m² + 3m + 3m + 1

Finally, we simplify by combining the like terms: 9m² + 6m + 1

Therefore, (3m + 1)² = 9m² + 6m + 1

The Significance of the Expansion

Expanding (3m + 1)² is valuable for various reasons:

  • Simplifying expressions: It allows us to rewrite the expression in a simpler form, making it easier to manipulate and solve equations.
  • Understanding patterns: The expansion reveals a specific pattern: the square of the first term, twice the product of the two terms, and the square of the second term. This pattern can be generalized to other binomial squares.
  • Applications in algebra and calculus: Expanding this expression is a fundamental skill required for more advanced mathematical concepts like factoring, solving quadratic equations, and finding derivatives.

Conclusion

By applying the FOIL method, we have successfully expanded (3m + 1)² to 9m² + 6m + 1. This process not only simplifies the expression but also highlights the underlying mathematical patterns and provides a stepping stone for further exploration in algebra and calculus.

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