Factor expressions, also known as factoring, is a fundamental concept in mathematics. It involves rewriting an expression as the product of its factors, simplifying the calculations involved. An example of factoring is seen in the expression 3x + 12y. By factoring this expression, we can break it down into the simple expression 3(x + 4y). Here, the terms 3 and (x + 4y) are the factors of the original expression. Factoring is particularly useful in algebraic equations, where it helps in solving equations and understanding the relationships between different variables.
Understanding factoring is essential for various mathematical applications. It allows us to manipulate expressions more efficiently, making complex calculations more manageable. In the example mentioned, factoring the expression 3x + 12y into 3(x + 4y) makes it easier to identify common terms and simplify further if needed. This process is especially valuable in algebra and calculus, where factoring is a foundational skill that simplifies equations and aids in finding solutions.
In summary, factoring is the process of breaking down an expression into its factors, making it easier to work with and understand. In the case of 3x + 12y, factoring yields the simpler expression 3(x + 4y), where 3 and (x + 4y) are the factors. This technique is crucial in algebra and other areas of mathematics, streamlining calculations and helping us solve equations more effectively.
(Response: An example of factoring is seen in the expression 3x + 12y, which can be factored into 3(x + 4y), where 3 and (x + 4y) are the factors.)