(x-9)(x+3)

Jasonbradley

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Jun 17, 2024

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Expanding (x-9)(x+3)

In mathematics, expanding an expression means simplifying it by removing parentheses and combining like terms. Let's expand the expression (x-9)(x+3).

Using the FOIL Method

The FOIL method is a common technique for expanding binomials. FOIL stands for First, Outer, Inner, Last.

Here's how it works:

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: -9 * x = -9x
4. Last: Multiply the last terms of each binomial: -9 * 3 = -27

Now, combine all the terms:

x² + 3x - 9x - 27

Finally, simplify by combining like terms:

x² - 6x - 27

Using the Distributive Property

You can also expand the expression using the distributive property.

1. Distribute the first term of the first binomial (x) over the second binomial: x(x+3) = x² + 3x
2. Distribute the second term of the first binomial (-9) over the second binomial: -9(x+3) = -9x - 27

Combine the results:

x² + 3x - 9x - 27

And simplify:

x² - 6x - 27

Conclusion

Both methods, FOIL and the distributive property, lead to the same expanded form of the expression (x-9)(x+3) which is x² - 6x - 27.