(x%2B7).jpeg "(x+7)(x+7)")
Expanding (x+7)(x+7)
The expression (x+7)(x+7) is a product of two binomials. To expand it, we can use the FOIL method, which stands for First, Outer, Inner, Last:
1. First: Multiply the first terms of each binomial: x * x = x²
2. Outer: Multiply the outer terms of the binomials: x * 7 = 7x
3. Inner: Multiply the inner terms of the binomials: 7 * x = 7x
4. Last: Multiply the last terms of each binomial: 7 * 7 = 49
Now, we add all the terms together:
x² + 7x + 7x + 49
Finally, combine the like terms:
x² + 14x + 49
Therefore, the expanded form of (x+7)(x+7) is x² + 14x + 49.
Understanding the Result
This expanded form represents a quadratic expression. It can also be written as (x+7)², which indicates that it is a perfect square trinomial.
Key points to remember about perfect square trinomials:
- They are the result of squaring a binomial.
- The coefficient of the middle term is double the product of the terms in the binomial.
- The constant term is the square of the constant term in the binomial.
In this case, the middle term (14x) is twice the product of x and 7, and the constant term (49) is the square of 7.
Applications
Understanding how to expand expressions like (x+7)(x+7) is crucial in algebra. It is used in various applications, including:
- Solving quadratic equations: Factoring quadratic expressions is often a key step in solving equations.
- Graphing quadratic functions: The expanded form of a quadratic expression helps identify the vertex and other key features of the graph.
- Calculus: Expanding expressions is essential in calculating derivatives and integrals.