(x-3)-distributive-property.jpeg "(x-6)(x-3) Distributive Property")
Understanding the Distributive Property: A Walkthrough with (x-6)(x-3)
The distributive property is a fundamental concept in algebra that allows us to simplify expressions involving multiplication. It states that multiplying a sum by a number is the same as multiplying each term of the sum by that number. In other words, a(b+c) = ab + ac.
Let's apply this property to expand the expression (x-6)(x-3).
Breaking it Down
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Identify the terms: We have two binomials: (x-6) and (x-3).
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Apply the distributive property:
- Multiply the first term of the first binomial (x) by each term of the second binomial (x and -3):
- x * x = x²
- x * -3 = -3x
- Multiply the second term of the first binomial (-6) by each term of the second binomial:
- -6 * x = -6x
- -6 * -3 = 18
- Multiply the first term of the first binomial (x) by each term of the second binomial (x and -3):
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Combine like terms: Now we have: x² - 3x - 6x + 18
- Combine the -3x and -6x terms: x² - 9x + 18
Final Result
Therefore, the expanded form of (x-6)(x-3) using the distributive property is x² - 9x + 18.
Why is this important?
Understanding the distributive property is crucial because:
- It simplifies expressions: We can convert complicated multiplications into simpler sums.
- It helps us solve equations: Expanding expressions is often necessary to solve equations.
- It forms the basis for other algebraic concepts: Many higher-level algebraic concepts are built upon the distributive property.
By consistently practicing and applying the distributive property, you'll become more confident in manipulating and understanding algebraic expressions.