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Factoring and Expanding (x-2)(x+7)
This article will explore the process of factoring and expanding the expression (x-2)(x+7).
Factoring
Factoring is the process of breaking down an expression into its multiplicative components. In this case, we are already given the factored form of the expression. This means that it is already in its simplest form, where the factors are multiplied together.
Expanding
Expanding, also known as multiplying out, involves removing the parentheses and combining like terms. To expand the expression (x-2)(x+7), we can use the FOIL method:
- First: Multiply the first terms of each binomial: x * x = x²
- Outer: Multiply the outer terms of the binomials: x * 7 = 7x
- Inner: Multiply the inner terms of the binomials: -2 * x = -2x
- Last: Multiply the last terms of each binomial: -2 * 7 = -14
Now, we combine all the terms:
x² + 7x - 2x - 14
Finally, combine the like terms:
x² + 5x - 14
Therefore, the expanded form of (x-2)(x+7) is x² + 5x - 14.
Summary
- The factored form of the expression is (x-2)(x+7).
- The expanded form of the expression is x² + 5x - 14.
- Factoring and expanding are inverse operations, meaning they undo each other.
This understanding of factoring and expanding is crucial in solving equations and simplifying expressions in algebra.