(n%2B3).jpeg "(2n+6)(n+3)")
Simplifying the Expression (2n+6)(n+3)
The expression (2n+6)(n+3) represents the product of two binomials. To simplify it, we can use the FOIL method, which stands for First, Outer, Inner, Last. This method helps us multiply each term in the first binomial by each term in the second binomial.
Applying FOIL
Let's break down the steps using FOIL:
- First: Multiply the first terms of each binomial: (2n) * (n) = 2n²
- Outer: Multiply the outer terms of the binomials: (2n) * (3) = 6n
- Inner: Multiply the inner terms of the binomials: (6) * (n) = 6n
- Last: Multiply the last terms of the binomials: (6) * (3) = 18
Now, we have: 2n² + 6n + 6n + 18
Combining Like Terms
The next step is to combine the like terms: 2n² + 12n + 18
Simplified Expression
Therefore, the simplified form of the expression (2n+6)(n+3) is 2n² + 12n + 18.
Further Considerations
- This simplified expression represents a quadratic equation because the highest power of the variable 'n' is 2.
- We can factor out a 2 from the expression: 2(n² + 6n + 9)
- This factored form can help in further analysis or solving for the roots of the equation.