%5E2.jpeg "(x+7/2)^2")
Expanding and Simplifying (x + 7/2)^2
The expression (x + 7/2)^2 represents the square of a binomial. To expand and simplify it, we can use the following methods:
1. Using the FOIL Method
FOIL stands for First, Outer, Inner, Last, and helps us multiply two binomials.
- First: Multiply the first terms of each binomial: x * x = x²
- Outer: Multiply the outer terms of the binomials: x * 7/2 = 7x/2
- Inner: Multiply the inner terms of the binomials: 7/2 * x = 7x/2
- Last: Multiply the last terms of each binomial: 7/2 * 7/2 = 49/4
Now, combine the terms:
x² + 7x/2 + 7x/2 + 49/4
Simplify by combining like terms:
x² + 7x + 49/4
2. Using the Square of a Sum Formula
The square of a sum formula states: (a + b)² = a² + 2ab + b²
In our case, a = x and b = 7/2. Applying the formula:
(x + 7/2)² = x² + 2(x)(7/2) + (7/2)²
Simplify:
x² + 7x + 49/4
Conclusion
Both methods lead to the same simplified expression: x² + 7x + 49/4. This expression represents the expanded form of (x + 7/2)².