(x-3)(x-9)

Jasonbradley

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Jun 17, 2024

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Expanding the Expression (x - 3)(x - 9)

This expression represents the product of two binomials: (x - 3) and (x - 9). To expand it, we can use the FOIL method, which stands for First, Outer, Inner, Last.

FOIL Method Breakdown

1. First: Multiply the first terms of each binomial: x * x = x²
2. Outer: Multiply the outer terms of the binomials: x * -9 = -9x
3. Inner: Multiply the inner terms of the binomials: -3 * x = -3x
4. Last: Multiply the last terms of each binomial: -3 * -9 = 27

Combining the Terms

Now we combine the terms we obtained:

x² - 9x - 3x + 27

Finally, we simplify by combining the like terms:

x² - 12x + 27

Conclusion

Therefore, the expanded form of (x - 3)(x - 9) is x² - 12x + 27. This expression can also be used to represent a quadratic equation, which can be further analyzed to find its roots, vertex, and other properties.