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(3x-1)(4x+5)

2 min read Jun 16, 2024
(3x-1)(4x+5)

Expanding the Expression (3x - 1)(4x + 5)

This article explores the process of expanding the algebraic expression (3x - 1)(4x + 5). We will utilize the FOIL method, a mnemonic for multiplying binomials, to achieve this.

FOIL Method Explained

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.

Applying FOIL to (3x - 1)(4x + 5)

Let's apply the FOIL method to our expression:

  1. First: (3x)(4x) = 12x²
  2. Outer: (3x)(5) = 15x
  3. Inner: (-1)(4x) = -4x
  4. Last: (-1)(5) = -5

Now, combine the results:

12x² + 15x - 4x - 5

Finally, simplify by combining like terms:

12x² + 11x - 5

Conclusion

By applying the FOIL method, we successfully expanded the expression (3x - 1)(4x + 5) to obtain the simplified form 12x² + 11x - 5. This process is a fundamental skill in algebra, allowing you to manipulate and solve various equations and expressions.

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