(1%E2%88%923x).jpeg "(6x+1)(1−3x)")
Expanding the Expression (6x + 1)(1 - 3x)
This article will explore the expansion of the expression (6x + 1)(1 - 3x). We will utilize the FOIL method, which stands for First, Outer, Inner, Last, to simplify the expression.
The FOIL Method
The FOIL method is a helpful mnemonic for remembering how to multiply two binomials. It provides a systematic way to multiply each term in the first binomial by each term in the second binomial:
- 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 (6x + 1)(1 - 3x):
- First: (6x) * (1) = 6x
- Outer: (6x) * (-3x) = -18x²
- Inner: (1) * (1) = 1
- Last: (1) * (-3x) = -3x
Now, we combine all the terms: 6x - 18x² + 1 - 3x
Finally, we arrange the terms in descending order of their exponents:
-18x² + 3x + 1
Therefore, the expanded form of the expression (6x + 1)(1 - 3x) is -18x² + 3x + 1.
Conclusion
Using the FOIL method, we successfully expanded the expression (6x + 1)(1 - 3x) into its simplified form, -18x² + 3x + 1. This method provides a straightforward approach to multiplying binomials and understanding the resulting polynomial.