(3x-2).jpeg "(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.