(x-3).jpeg "(2x+7)(x-3)")
Expanding the Expression (2x+7)(x-3)
This article will guide you through the process of expanding the expression (2x+7)(x-3). This involves applying the distributive property, also known as the FOIL method, which stands for First, Outer, Inner, Last.
Understanding the Distributive Property
The distributive property states that multiplying a sum by a number is the same as multiplying each addend separately by the number and then adding the products together.
In simpler terms, it means: a(b + c) = ab + ac
Expanding the Expression
Let's break down the expansion of (2x+7)(x-3) step-by-step:
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First: Multiply the first terms of each binomial: 2x * x = 2x²
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Outer: Multiply the outer terms of the binomials: 2x * -3 = -6x
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Inner: Multiply the inner terms of the binomials: 7 * x = 7x
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Last: Multiply the last terms of each binomial: 7 * -3 = -21
Now, we have: 2x² - 6x + 7x - 21
Finally, combine the like terms: 2x² + x - 21
Conclusion
Therefore, the expanded form of (2x+7)(x-3) is 2x² + x - 21.
By understanding the distributive property and applying the FOIL method, you can effectively expand and simplify algebraic expressions.