%5E2-as-a-trinomial-in-standard-form.jpeg "(x+10)^2 As A Trinomial In Standard Form")
Expanding (x+10)^2 into a Trinomial
The expression (x+10)^2 represents the square of the binomial (x+10). To expand this expression and write it as a trinomial in standard form, we can use the following steps:
1. Understanding the Concept
Recall that squaring a binomial means multiplying it by itself. Therefore, (x+10)^2 is equivalent to (x+10)(x+10).
2. Applying the Distributive Property
We can use the distributive property (often referred to as FOIL - First, Outer, Inner, Last) to multiply the binomials:
- First: x * x = x^2
- Outer: x * 10 = 10x
- Inner: 10 * x = 10x
- Last: 10 * 10 = 100
Adding these terms together, we get: x^2 + 10x + 10x + 100
3. Combining Like Terms
Finally, combine the like terms (10x + 10x) to simplify the expression:
x^2 + 20x + 100
Therefore, the trinomial in standard form for (x+10)^2 is x^2 + 20x + 100.
Key Points to Remember:
- Squaring a binomial: (a + b)^2 = a^2 + 2ab + b^2
- Standard form of a trinomial: ax^2 + bx + c, where a, b, and c are constants.
Understanding how to expand binomials into trinomials is crucial for various algebraic operations, including solving quadratic equations, factoring polynomials, and working with quadratic functions.