%5E2-as-a-trinomial-in-standard-form.jpeg "(x+6)^2 As A Trinomial In Standard Form")
Expanding (x+6)^2 into a Trinomial
The expression (x+6)^2 represents the square of the binomial (x+6). To expand this expression and express it as a trinomial in standard form, we can use the following methods:
1. Using the FOIL method:
FOIL stands for First, Outer, Inner, Last. It is a mnemonic device to remember the steps involved in multiplying two binomials.
- First: Multiply the first terms of each binomial: x * x = x^2
- Outer: Multiply the outer terms of the binomials: x * 6 = 6x
- Inner: Multiply the inner terms of the binomials: 6 * x = 6x
- Last: Multiply the last terms of each binomial: 6 * 6 = 36
Now, add all the terms together: x^2 + 6x + 6x + 36
Finally, combine the like terms: x^2 + 12x + 36
2. Using the Square of a Binomial Formula:
The square of a binomial formula states: (a + b)^2 = a^2 + 2ab + b^2
In our case, a = x and b = 6.
Substituting these values into the formula:
(x + 6)^2 = x^2 + 2(x)(6) + 6^2
Simplifying: x^2 + 12x + 36
Conclusion
Both methods lead us to the same result: (x + 6)^2 expanded as a trinomial in standard form is x^2 + 12x + 36. This expression is a quadratic trinomial with a leading coefficient of 1, a linear coefficient of 12, and a constant term of 36.