(n%2B3).jpeg "(7n-2)(n+3)")
Expanding the Expression (7n - 2)(n + 3)
This article will walk you through the process of expanding the expression (7n - 2)(n + 3). This type of expression is called a binomial product, and we can use the FOIL method to simplify it.
What is FOIL?
FOIL is an acronym that stands for First, Outer, Inner, Last. This method helps us remember 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 two binomials.
- Inner: Multiply the inner terms of the two binomials.
- Last: Multiply the last terms of each binomial.
Expanding (7n - 2)(n + 3)
Let's apply FOIL to our expression:
- First: (7n)(n) = 7n²
- Outer: (7n)(3) = 21n
- Inner: (-2)(n) = -2n
- Last: (-2)(3) = -6
Now we have: 7n² + 21n - 2n - 6
Finally, combine the like terms: 7n² + 19n - 6
Conclusion
By using the FOIL method, we have successfully expanded the expression (7n - 2)(n + 3) to obtain 7n² + 19n - 6. This technique is essential for simplifying polynomial expressions and solving various algebraic problems.