(x-4)-in-standard-form.jpeg "(2x+3)(x-4) In Standard Form")
Expanding and Simplifying (2x+3)(x-4)
In this article, we'll learn how to expand the expression (2x+3)(x-4) and rewrite it in standard form.
Expanding using FOIL
The FOIL method is a helpful acronym to remember the steps for expanding products of binomials:
- First: Multiply the first terms of each binomial: 2x * x = 2x²
- Outer: Multiply the outer terms of the binomials: 2x * -4 = -8x
- Inner: Multiply the inner terms of the binomials: 3 * x = 3x
- Last: Multiply the last terms of each binomial: 3 * -4 = -12
Now, we have: (2x+3)(x-4) = 2x² - 8x + 3x - 12
Simplifying the expression
Combine the like terms (-8x and 3x):
2x² - 8x + 3x - 12 = 2x² - 5x - 12
Standard Form
The standard form of a polynomial is written with the terms arranged in descending order of their exponents. In this case, our expression is already in standard form:
2x² - 5x - 12
Therefore, the expression (2x+3)(x-4) expanded and written in standard form is 2x² - 5x - 12.