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(a-1)(2a+5)

2 min read Jun 16, 2024
(a-1)(2a+5)

Expanding the Expression (a-1)(2a+5)

This article will explore the process of expanding the expression (a-1)(2a+5), which is a product of two binomials. This expansion is a fundamental concept in algebra, often encountered in solving equations, simplifying expressions, and working with quadratic functions.

The FOIL Method

The most common method for expanding such expressions is the FOIL method. FOIL stands for:

  • First: Multiply the first terms of each binomial.
  • Outer: Multiply the outer terms of the binomials.
  • Inner: Multiply the inner terms of the binomials.
  • Last: Multiply the last terms of each binomial.

Let's apply FOIL to our expression:

F: (a) * (2a) = 2a² O: (a) * (5) = 5a I: (-1) * (2a) = -2a L: (-1) * (5) = -5

Now, we combine the terms:

2a² + 5a - 2a - 5

Finally, we simplify by combining like terms:

2a² + 3a - 5

Conclusion

By using the FOIL method, we have successfully expanded the expression (a-1)(2a+5) into its simplified form, 2a² + 3a - 5. This process demonstrates a fundamental algebraic technique with applications in various mathematical contexts.

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