(x-3)-in-standard-form.jpeg "(x+3)(x-3) In Standard Form")
Expanding (x+3)(x-3) into Standard Form
The expression (x+3)(x-3) represents the product of two binomials. To express it in standard form, we need to expand the product and simplify it.
Using the FOIL Method
The FOIL method is a common technique for multiplying binomials. It stands for First, Outer, Inner, Last, which represent the terms we multiply:
- First: Multiply the first terms of each binomial: x * x = x²
- Outer: Multiply the outer terms of the binomials: x * -3 = -3x
- Inner: Multiply the inner terms of the binomials: 3 * x = 3x
- Last: Multiply the last terms of each binomial: 3 * -3 = -9
Now, we combine the terms: x² - 3x + 3x - 9
Notice that the -3x and 3x terms cancel each other out. This leaves us with:
x² - 9
Understanding the Pattern
The expression (x+3)(x-3) is a special case of the difference of squares pattern:
(a + b)(a - b) = a² - b²
In our case, a = x and b = 3. This pattern is useful to recognize because it allows us to quickly expand expressions of this form.
Standard Form
The final expression, x² - 9, is in standard form. It is a quadratic polynomial with the highest power of x being 2, followed by a constant term.
In summary, (x+3)(x-3) expands to x² - 9 in standard form. This demonstrates the difference of squares pattern, which can be used to simplify similar expressions.