%5E2.jpeg "(x+15)^2")
Expanding (x+15)^2
The expression (x+15)^2 represents the square of the binomial (x+15). To expand this expression, we can use the FOIL method or the square of a binomial pattern.
Using the FOIL Method
FOIL stands for First, Outer, Inner, Last. This method helps us multiply each term of the first binomial with each term of the second binomial:
- First: x * x = x^2
- Outer: x * 15 = 15x
- Inner: 15 * x = 15x
- Last: 15 * 15 = 225
Combining the terms, we get:
(x+15)^2 = x^2 + 15x + 15x + 225
Simplifying the expression:
(x+15)^2 = x^2 + 30x + 225
Using the Square of a Binomial Pattern
The square of a binomial pattern states:
(a + b)^2 = a^2 + 2ab + b^2
Applying this pattern to our expression:
(x+15)^2 = x^2 + 2(x)(15) + 15^2
Simplifying:
(x+15)^2 = x^2 + 30x + 225
Conclusion
Both methods result in the same expanded expression: x^2 + 30x + 225. This expanded form is a trinomial with a leading coefficient of 1, a linear coefficient of 30, and a constant term of 225. It's important to remember that expanding a squared binomial often simplifies the expression and makes it easier to work with in further calculations or analysis.