(2x-7)-in-standard-form.jpeg "(2x-3)(2x-7) In Standard Form")
Expanding and Simplifying (2x-3)(2x-7) into Standard Form
This article will guide you through the process of expanding and simplifying the expression (2x-3)(2x-7) into standard form, a polynomial expression where terms are arranged from highest to lowest degree.
Understanding Standard Form
Standard form for a polynomial is where terms are arranged in descending order of their exponents. For example, a quadratic equation in standard form looks like this:
ax² + bx + c
Where 'a', 'b', and 'c' are constants and 'x' is a variable.
Expanding the Expression
To expand the expression (2x-3)(2x-7), we can use the FOIL method:
- First: Multiply the first terms of each binomial: (2x) * (2x) = 4x²
- Outer: Multiply the outer terms: (2x) * (-7) = -14x
- Inner: Multiply the inner terms: (-3) * (2x) = -6x
- Last: Multiply the last terms: (-3) * (-7) = 21
Combining these results gives us:
4x² - 14x - 6x + 21
Simplifying the Expression
Now, we combine like terms (-14x and -6x) to simplify the expression:
4x² - 20x + 21
Final Answer
Therefore, (2x-3)(2x-7) expanded and simplified into standard form is 4x² - 20x + 21.