%5E2.jpeg "(2+5n^2)^2")
Expanding the Expression (2 + 5n^2)^2
The expression (2 + 5n^2)^2 represents the square of a binomial. To expand this expression, we can use the FOIL method or the square of a binomial formula.
1. Using the FOIL Method
FOIL stands for First, Outer, Inner, Last. This method involves multiplying each term of the first binomial with each term of the second binomial.
- First: 2 * 2 = 4
- Outer: 2 * 5n^2 = 10n^2
- Inner: 5n^2 * 2 = 10n^2
- Last: 5n^2 * 5n^2 = 25n^4
Adding all the terms together, we get:
(2 + 5n^2)^2 = 4 + 10n^2 + 10n^2 + 25n^4
2. Using the Square of a Binomial Formula
The square of a binomial formula states that:
(a + b)^2 = a^2 + 2ab + b^2
In this case, a = 2 and b = 5n^2. Substituting these values into the formula, we get:
(2 + 5n^2)^2 = 2^2 + 2(2)(5n^2) + (5n^2)^2
Simplifying the expression:
(2 + 5n^2)^2 = 4 + 20n^2 + 25n^4
Conclusion
Both methods lead to the same result:
(2 + 5n^2)^2 = 4 + 20n^2 + 25n^4
This expanded form represents the polynomial expression equivalent to the original squared binomial. It is important to remember that this expanded form allows for easier manipulation and further calculations if needed.