(x+7)(x+3)

2 min read Jun 17, 2024
(x+7)(x+3)

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.

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