(x%2B3).jpeg "(x-5)(x+3)")
Factoring and Expanding: (x-5)(x+3)
This expression represents the multiplication of two binomials: (x-5) and (x+3). Let's explore how to factor and expand it.
Expanding the Expression
To expand the expression, we use the FOIL method:
- First: Multiply the first terms of each binomial: x * x = x²
- Outer: Multiply the outer terms of the binomials: x * 3 = 3x
- Inner: Multiply the inner terms of the binomials: -5 * x = -5x
- Last: Multiply the last terms of each binomial: -5 * 3 = -15
Now, combine the terms:
x² + 3x - 5x - 15
Simplify by combining like terms:
x² - 2x - 15
Therefore, the expanded form of (x-5)(x+3) is x² - 2x - 15.
Factoring the Expression
We can also factor the expression x² - 2x - 15 back into its original binomial form. Here's how:
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Find two numbers that multiply to -15 and add up to -2. These numbers are -5 and 3.
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Rewrite the expression using these numbers: x² - 5x + 3x - 15
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Factor by grouping: x(x-5) + 3(x-5)
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Factor out the common binomial: (x-5)(x+3)
Therefore, the factored form of x² - 2x - 15 is (x-5)(x+3).
Conclusion
Expanding and factoring are important skills in algebra. By understanding the FOIL method and factoring techniques, you can manipulate expressions like (x-5)(x+3) to reveal their expanded or factored forms.