## 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:

**F**irst: Multiply the first terms of each binomial.**O**uter: Multiply the outer terms of the binomials.**I**nner: Multiply the inner terms of the binomials.**L**ast: 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**.