Final answer:
Factoring an expression in mathematics involves breaking it down into simpler terms or products. This process simplifies expressions, solves equations, and makes computations and unit conversions easier.
Step-by-step explanation:
Understanding Factoring in Mathematics
To factor an expression in mathematics means to break it down into simpler terms or products that, when multiplied together, result in the original expression. This is similar to dividing a pie into pieces, where each piece represents a factor of the whole. For instance, when we look at the expression 15x², we can factor it into 3⋅ 5⋅ x⋅ x, where each number and variable represents a factor that contributes to the overall expression.
Factoring is often used to simplify expressions, solve equations, and make certain computations easier to understand. It is essential for various aspects of algebra, including solving quadratic equations, rational expressions, and more. For example, the equation x² - 4 can be factored to (x + 2)(x - 2), which reveals more information about the possible values of x.
When working with fractions, the concept of factoring remains important. For example, if we multiply fractions, we multiply the numerators together and the denominators together, simplifying by common factors as necessary. This can also apply when using the factor-label method for unit conversions in subjects like chemistry, where we multiply by identities to achieve the desired units.