%5E2-as-a-trinomial-in-standard-form.jpeg "(x+12)^2 As A Trinomial In Standard Form")
Expanding (x + 12)^2 into a Trinomial
The expression (x + 12)^2 represents the square of a binomial. To express this in standard trinomial form, we need to expand it using the distributive property or by recognizing a pattern.
Using the Distributive Property
We can expand (x + 12)^2 by multiplying it by itself:
(x + 12)^2 = (x + 12)(x + 12)
Now, we can use the distributive property (also known as FOIL) to multiply the terms:
- First: x * x = x^2
- Outer: x * 12 = 12x
- Inner: 12 * x = 12x
- Last: 12 * 12 = 144
Combining like terms, we get:
x^2 + 12x + 12x + 144 = x^2 + 24x + 144
Using the Pattern
We can also recognize that squaring a binomial follows a specific pattern:
(a + b)^2 = a^2 + 2ab + b^2
In our case, a = x and b = 12. Applying the pattern, we get:
x^2 + 2(x)(12) + 12^2 = x^2 + 24x + 144
Conclusion
Both methods lead us to the same result: (x + 12)^2 expanded in standard trinomial form is x^2 + 24x + 144. This form is useful for simplifying expressions, solving equations, and understanding the relationship between different algebraic forms.