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(2x-9)(3x-5)

2 min read Jun 16, 2024
(2x-9)(3x-5)

Expanding the Expression: (2x-9)(3x-5)

This article will guide you through the process of expanding the expression (2x-9)(3x-5), which involves multiplying two binomials.

Understanding the Process

The expression (2x-9)(3x-5) represents the product of two binomials. To expand this, we need to apply the distributive property (also known as 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.

Applying FOIL

Let's apply the FOIL method to our expression:

  • First: (2x)(3x) = 6x²
  • Outer: (2x)(-5) = -10x
  • Inner: (-9)(3x) = -27x
  • Last: (-9)(-5) = 45

Now, we combine the results:

6x² - 10x - 27x + 45

Finally, combine the like terms:

6x² - 37x + 45

Conclusion

Therefore, the expanded form of (2x-9)(3x-5) is 6x² - 37x + 45. By applying the distributive property (FOIL method), we successfully multiplied the two binomials and obtained the simplified polynomial expression.

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