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Chapter 1: Problem 86

What does it mean to simplify an algebraic expression?

Short Answer

Expert verified
Simplifying an algebraic expression means rewriting it in a more understandable or solvable form - typically with the fewest terms or variables possible - all the while maintaining its original value. It can include combining like terms, applying the distributive property, reducing fractions, and cancelling out common factors.

Step by step solution

01

- Understanding Algebraic Expressions

An algebraic expression is a mathematical phrase that combines numbers, variables (letters that represent unknown numbers), and operations such as addition, subtraction, multiplication, and division. Examples include \(3x+2y\), \(5p^2q^3\), or even single numbers or variables, such as 7 or \(x\).
02

- What does it mean to simplify?

To simplify an algebraic expression means to rewrite it in a manner that makes it easier to understand or solve. In other words, to make it 'simpler'. Simplification can include processes like combining like terms, using the distributive property, removing parentheses, reducing fractions, and cancelling out common factors, provided these operations maintain the equality or value of the original expression. For example, the expression \(3x+2x\) can be simplified to \(5x\) by combining like terms.
03

- Importance of simplifying algebraic expressions

Simplifying algebraic expressions is important because it can assist in understanding the properties of the equation, equation solution, making computations more manageable, and revealing the most 'direct route' to the answer. It's a key tool for mathematicians, scientists, and engineers when solving complex problems, and it serves as a foundation for more advanced mathematical concepts.

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Most popular questions from this chapter

Simplify each algebraic expression. $$4+7 y-17 y$$

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