(x%2B10)-in-standard-form.jpeg "(x-10)(x+10) In Standard Form")
Expanding (x-10)(x+10) into Standard Form
The expression (x-10)(x+10) is in factored form. To rewrite it in standard form, we need to expand it using the distributive property (often referred to as FOIL).
FOIL stands for First, Outer, Inner, Last, which helps us remember the order of multiplication.
- First: Multiply the first terms of each binomial: x * x = x²
- Outer: Multiply the outer terms of the binomials: x * 10 = 10x
- Inner: Multiply the inner terms of the binomials: -10 * x = -10x
- Last: Multiply the last terms of each binomial: -10 * 10 = -100
Now, we have: x² + 10x - 10x - 100
Finally, combine the like terms: x² - 100
Therefore, the standard form of (x-10)(x+10) is x² - 100.
Important Note: This expression is a special case called the difference of squares. The pattern is (a-b)(a+b) = a² - b².
Understanding this pattern can help you quickly expand similar expressions without going through the full FOIL process.