(2x+3)(3x-2)

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

Expanding the Expression: (2x+3)(3x-2)

This article will guide you through the process of expanding the expression (2x+3)(3x-2).

Understanding the Problem

We have two binomials, (2x+3) and (3x-2), multiplied together. Expanding this expression means multiplying each term in the first binomial by each term in the second binomial.

Using the FOIL Method

The FOIL method is a helpful mnemonic for expanding binomials:

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

Applying FOIL to our expression:

  • F: (2x) * (3x) = 6x²
  • O: (2x) * (-2) = -4x
  • I: (3) * (3x) = 9x
  • L: (3) * (-2) = -6

Combining Like Terms

Now we have: 6x² - 4x + 9x - 6

Combining the like terms (-4x and 9x) gives us:

6x² + 5x - 6

Final Answer

Therefore, the expanded form of (2x+3)(3x-2) is 6x² + 5x - 6.

Key Takeaways

  • The FOIL method provides a structured approach for expanding binomials.
  • Remember to combine like terms after applying the FOIL method.

This process can be applied to any expression involving the multiplication of two binomials.

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