(x%2B5)-answer.jpeg "(x+5)(x+5) Answer")
Expanding the Expression (x+5)(x+5)
This expression is a perfect square trinomial, meaning it represents the product of the same binomial multiplied by itself. Let's explore how to expand it:
Using the FOIL Method
FOIL stands for First, Outer, Inner, Last. This method helps us systematically multiply each term of the first binomial with each term of the second binomial:
- First: Multiply the first terms of each binomial: x * x = x²
- Outer: Multiply the outer terms of the binomials: x * 5 = 5x
- Inner: Multiply the inner terms of the binomials: 5 * x = 5x
- Last: Multiply the last terms of each binomial: 5 * 5 = 25
Now, we add all the results together:
x² + 5x + 5x + 25
Finally, combine the like terms:
x² + 10x + 25
Therefore, the expanded form of (x+5)(x+5) is x² + 10x + 25.
Using the Square of a Binomial Formula
We can also use the formula for the square of a binomial:
(a + b)² = a² + 2ab + b²
In this case, a = x and b = 5. Substituting these values into the formula, we get:
(x + 5)² = x² + 2(x)(5) + 5²
Simplifying, we obtain the same result as before:
x² + 10x + 25
Both methods lead to the same answer, so you can choose whichever one you find easier to understand and apply.