(x%2B7)-in-standard-form.jpeg "(x+2)(x+7) In Standard Form")
Expanding and Simplifying (x+2)(x+7) into Standard Form
In mathematics, the standard form of a quadratic expression is ax² + bx + c, where a, b, and c are constants. Let's expand and simplify the expression (x+2)(x+7) to achieve this form.
Using the FOIL Method
The FOIL method is a mnemonic for multiplying binomials:
- 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.
Applying this to (x+2)(x+7):
- First: x * x = x²
- Outer: x * 7 = 7x
- Inner: 2 * x = 2x
- Last: 2 * 7 = 14
Now we combine the terms: x² + 7x + 2x + 14
Finally, we simplify by combining the like terms:
x² + 9x + 14
Therefore, the standard form of (x+2)(x+7) is x² + 9x + 14.
Alternative Methods
While the FOIL method is commonly used, there are other approaches to expand the expression:
- Distributive Property: Distribute each term of the first binomial to the second binomial.
- Box Method: Organize the multiplication using a visual grid.
Both these methods will lead to the same simplified expression: x² + 9x + 14.