(x+12)^2 As A Trinomial

Jasonbradley

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Jun 16, 2024

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Expanding (x + 12)^2 as a Trinomial

The expression (x + 12)^2 represents the square of the binomial (x + 12). To expand it as a trinomial, we can utilize the FOIL method or the square of a binomial formula.

Using the FOIL Method

FOIL stands for First, Outer, Inner, Last. This method helps us multiply two binomials. Let's apply it to (x + 12)^2:

1. First: Multiply the first terms of each binomial: x * x = x^2
2. Outer: Multiply the outer terms: x * 12 = 12x
3. Inner: Multiply the inner terms: 12 * x = 12x
4. Last: Multiply the last terms: 12 * 12 = 144

Now, add all the results together:

x^2 + 12x + 12x + 144

Combining like terms:

x^2 + 24x + 144

Therefore, (x + 12)^2 expanded as a trinomial is x^2 + 24x + 144.

Using the Square of a Binomial Formula

The square of a binomial formula states: (a + b)^2 = a^2 + 2ab + b^2

Applying this formula to (x + 12)^2, where a = x and b = 12:

(x + 12)^2 = x^2 + 2(x)(12) + 12^2

Simplifying:

x^2 + 24x + 144

Both methods lead to the same result: (x + 12)^2 = x^2 + 24x + 144.

This trinomial represents the expanded form of the squared binomial.