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Expanding and Simplifying (x+7)(x+3)
In algebra, we often encounter expressions that involve multiplying binomials. One such example is (x+7)(x+3). Let's learn how to expand and simplify this expression.
Understanding the Concept
The expression (x+7)(x+3) represents the product of two binomials: (x+7) and (x+3). To expand this, we can use the distributive property (also known as FOIL method).
Using the Distributive Property (FOIL)
The FOIL method helps us remember the steps involved in expanding:
- 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. (7 * x) = 7x
- Last: Multiply the last terms of each binomial. (7 * 3) = 21
Combining Like Terms
Now, let's combine the terms we obtained:
x² + 3x + 7x + 21
The terms 3x and 7x are like terms. Combining them gives:
x² + 10x + 21
Final Result
Therefore, the expanded and simplified form of (x+7)(x+3) is x² + 10x + 21.
Application
Understanding how to expand and simplify expressions like (x+7)(x+3) is crucial in various mathematical contexts. This skill is essential for solving equations, working with quadratic functions, and understanding polynomial expressions.