%5E2-in-standard-form.jpeg "(x+6)^2 In Standard Form")
Expanding (x + 6)^2 into Standard Form
The expression (x + 6)^2 represents the square of the binomial (x + 6). To write this in standard form, we need to expand it and simplify.
Expanding the Expression
The expression (x + 6)^2 is equivalent to multiplying (x + 6) by itself:
(x + 6)^2 = (x + 6)(x + 6)
We can use the FOIL method (First, Outer, Inner, Last) to expand this product:
- First: x * x = x^2
- Outer: x * 6 = 6x
- Inner: 6 * x = 6x
- Last: 6 * 6 = 36
Combining the terms, we get:
x^2 + 6x + 6x + 36
Simplifying the Expression
Finally, we can simplify the expression by combining the like terms:
x^2 + 12x + 36
Standard Form
Therefore, the standard form of (x + 6)^2 is x^2 + 12x + 36.
This form highlights the coefficient of the quadratic term (1), the linear term (12), and the constant term (36). It is often useful for solving equations, graphing parabolas, and other mathematical operations.