(x+3)^2 As A Trinomial In Standard Form

Jasonbradley

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Jun 16, 2024

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Expanding (x+3)^2 into a Trinomial

The expression (x+3)^2 represents the square of the binomial (x+3). To expand this expression into a trinomial in standard form, we can use the FOIL method or the square of a binomial formula.

Using the FOIL Method

FOIL stands for First, Outer, Inner, Last, which describes the order in which we multiply the terms of the binomials.

1. First: Multiply the first terms of each binomial: x * x = x^2
2. Outer: Multiply the outer terms of the binomials: x * 3 = 3x
3. Inner: Multiply the inner terms of the binomials: 3 * x = 3x
4. Last: Multiply the last terms of each binomial: 3 * 3 = 9

Now we add all the products together: x^2 + 3x + 3x + 9

Finally, combine the like terms: x^2 + 6x + 9

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 = 3. Applying the formula:

x^2 + 2(x)(3) + 3^2

Simplifying the expression: x^2 + 6x + 9

Conclusion

Both methods lead to the same result: (x+3)^2 expands to the trinomial x^2 + 6x + 9 in standard form.