%5E2.jpeg "(5+x)^2")
Expanding (5 + x)^2
The expression (5 + x)^2 is a common mathematical expression that represents the square of the binomial (5 + x). To understand its meaning and how to expand it, let's break it down.
Understanding the Concept
The expression (5 + x)^2 means multiplying the binomial (5 + x) by itself:
(5 + x)^2 = (5 + x) * (5 + x)
Expanding the Expression
To expand the expression, we use the FOIL method, which stands for First, Outer, Inner, Last.
- First: Multiply the first terms of each binomial: 5 * 5 = 25
- Outer: Multiply the outer terms of the binomials: 5 * x = 5x
- Inner: Multiply the inner terms of the binomials: x * 5 = 5x
- Last: Multiply the last terms of each binomial: x * x = x^2
Now, combine the terms: 25 + 5x + 5x + x^2
Finally, simplify by combining the like terms: 25 + 10x + x^2
The Result
Therefore, the expanded form of (5 + x)^2 is 25 + 10x + x^2. This expression is a trinomial, which is a polynomial with three terms.
Generalization
The expansion of (5 + x)^2 can be generalized to any binomial:
(a + b)^2 = a^2 + 2ab + b^2
This formula allows you to easily expand any binomial squared without going through the FOIL method each time.