(x+3)2 Answer

Jasonbradley

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Jun 16, 2024

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Expanding (x + 3)²

The expression (x + 3)² represents the square of the binomial (x + 3). To find the answer, we need to expand this expression using the FOIL method or by using the square of a binomial formula.

Using the FOIL Method

FOIL stands for First, Outer, Inner, Last. This method helps us multiply two binomials systematically:

1. First: Multiply the first terms of each binomial: x * x = x²
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, add all the terms together: x² + 3x + 3x + 9

Finally, combine the like terms: x² + 6x + 9

Using the Square of a Binomial Formula

The square of a binomial formula states: (a + b)² = a² + 2ab + b²

In our case, a = x and b = 3. Applying the formula:

(x + 3)² = x² + 2(x)(3) + 3²

Simplifying: x² + 6x + 9

Conclusion

Both methods lead to the same answer: (x + 3)² = x² + 6x + 9. Expanding the expression reveals the trinomial form which can be useful for various mathematical operations and applications.