(2n+3)(2n+1)

Jasonbradley

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Jun 16, 2024

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Expanding the Expression (2n+3)(2n+1)

In mathematics, expanding an expression often refers to simplifying it by removing parentheses and combining like terms. This process is crucial for solving equations, simplifying formulas, and performing other algebraic operations. Today, we will explore how to expand the expression (2n+3)(2n+1).

Using the FOIL Method

The FOIL method is a popular technique for expanding products of two binomials. FOIL stands for First, Outer, Inner, Last, which describes the order in which you multiply the terms:

1. First: Multiply the first terms of each binomial: (2n) * (2n) = 4n²
2. Outer: Multiply the outer terms of the binomials: (2n) * (1) = 2n
3. Inner: Multiply the inner terms of the binomials: (3) * (2n) = 6n
4. Last: Multiply the last terms of each binomial: (3) * (1) = 3

Now, combine all the terms: 4n² + 2n + 6n + 3

Finally, simplify by combining like terms: 4n² + 8n + 3

Therefore, the expanded form of (2n+3)(2n+1) is 4n² + 8n + 3.

Alternative Methods

While the FOIL method is widely used, there are other approaches to expanding this expression. One method involves distributing each term of the first binomial across the second binomial.

• Distributing (2n+3):

  • (2n) * (2n+1) = 4n² + 2n
  • (3) * (2n+1) = 6n + 3

• Combine the results: 4n² + 2n + 6n + 3 = 4n² + 8n + 3

The result is the same as obtained with the FOIL method.

Conclusion

Expanding expressions like (2n+3)(2n+1) is a fundamental skill in algebra. By applying methods like FOIL or distribution, we can simplify the expression into a more manageable form. This process is essential for solving equations, manipulating formulas, and understanding the relationships between different mathematical concepts.