(x%2B6)-distributive-property.jpeg "(x-4)(x+6) Distributive Property")
Using the Distributive Property to Multiply (x-4)(x+6)
The distributive property is a fundamental tool in algebra that allows us to multiply expressions involving multiple terms. In this case, we'll use it to expand the product of the binomials (x - 4) and (x + 6).
Understanding the Distributive Property
The distributive property states that for any numbers a, b, and c:
a(b + c) = ab + ac
This means we can distribute the "a" to both terms inside the parentheses.
Applying the Property to (x-4)(x+6)
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Treat (x-4) as a single term. We'll distribute this term to both terms inside the second binomial:
(x-4)(x+6) = (x-4) * x + (x-4) * 6
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Distribute again. Now we need to distribute the "x" and the "-4" individually to the terms inside their respective parentheses:
(x-4) * x + (x-4) * 6 = x * x + (-4) * x + x * 6 + (-4) * 6
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Simplify. Multiply the terms and combine like terms:
x² - 4x + 6x - 24 = x² + 2x - 24
Conclusion
By applying the distributive property twice, we have successfully expanded the product (x-4)(x+6) to the simplified expression x² + 2x - 24. This process illustrates how the distributive property is a powerful tool for simplifying and manipulating algebraic expressions.