(x-3)^2 Expand

Jasonbradley

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Jun 17, 2024

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Expanding (x-3)^2

The expression (x-3)^2 represents the square of the binomial (x-3). To expand this, we can use the FOIL method or the square of a binomial formula.

Using the FOIL Method

FOIL stands for First, Outer, Inner, Last. It's a mnemonic for multiplying two binomials.

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

Now, combine the results:

x^2 - 3x - 3x + 9

Finally, simplify by combining 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

Applying this formula to our expression:

a = x b = 3

(x - 3)^2 = x^2 - 2(x)(3) + 3^2

Simplifying:

x^2 - 6x + 9

Conclusion

Both methods, FOIL and the square of a binomial formula, lead to the same expanded form of (x-3)^2, which is x^2 - 6x + 9. You can choose whichever method you find easier to understand and apply.