(3i-1).jpeg "(3i+4)(3i-1)")
Expanding the Expression: (3i + 4)(3i - 1)
This article will guide you through the process of expanding the expression (3i + 4)(3i - 1) using the FOIL method (First, Outer, Inner, Last).
Understanding the FOIL Method
The FOIL method is a mnemonic device used to remember the order of operations when multiplying two binomials. It 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.
Expanding the Expression
Let's apply the FOIL method to our expression: (3i + 4)(3i - 1)
1. First: (3i) * (3i) = 9i²
2. Outer: (3i) * (-1) = -3i
3. Inner: (4) * (3i) = 12i
4. Last: (4) * (-1) = -4
Now, let's combine all the terms:
9i² - 3i + 12i - 4
Simplify by combining like terms:
9i² + 9i - 4
Remember that i² = -1. Substitute this into the expression:
9(-1) + 9i - 4
Simplify:
-9 + 9i - 4
Final Answer:
-13 + 9i
Conclusion
By applying the FOIL method, we expanded the expression (3i + 4)(3i - 1) and obtained the simplified result of -13 + 9i. This demonstrates the importance of understanding the FOIL method when working with binomials.