(x%2B7).jpeg "(x-3)(x+7)")
Expanding and Simplifying (x - 3)(x + 7)
This expression represents the product of two binomials: (x - 3) and (x + 7). To simplify it, we'll use the FOIL method:
First: Multiply the first terms of each binomial. Outer: Multiply the outer terms of the binomials. Inner: Multiply the inner terms of the binomials. Last: Multiply the last terms of each binomial.
Let's apply FOIL to our expression:
F: (x)(x) = x² O: (x)(7) = 7x I: (-3)(x) = -3x L: (-3)(7) = -21
Now, we combine the terms:
x² + 7x - 3x - 21
Finally, we simplify by combining the like terms:
x² + 4x - 21
Therefore, the expanded and simplified form of (x - 3)(x + 7) is x² + 4x - 21.
Understanding the Result
This expression represents a quadratic equation, which is a polynomial with the highest power of the variable being 2. The equation can be used to model various real-world situations, such as the trajectory of a projectile or the area of a rectangle.
By factoring the original expression, we have derived the simplified form, which is easier to work with and understand. This process is crucial in various mathematical and scientific applications.