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Chapter 6: Problem 79

What does it mean to simplify an algebraic expression?

Short Answer

Expert verified
Simplifying an algebraic expression means to reduce it to the simplest form. This generally involves combining like terms (terms with the same variables and powers), or carrying out operations like addition, subtraction, multiplication, and division. The process can make algebraic expressions shorter, easier to understand and solve.

Step by step solution

01

Understanding Simplification

Simplifying an algebraic expression means to reduce it to its simplest form. This can involve combining like terms, which are terms with the same variables and powers, or carrying out operations like addition, subtraction, multiplication, and division. For example, if given the expression \(5x + 3x\), this could be simplified to \(8x\) by combining like terms.
02

Realizing the Value of Simplifying

Simplification is the process of making an algebraic expression shorter, easier to understand and more efficient. In algebra, you will often be asked to simplify expressions as a first step to solve an equation. This is because it makes the equation easier to understand and solve.
03

Demonstrating simplification

Let's take an example to demonstrate how to simplify an algebraic expression. Consider the expression \(3x + 2x + 7 + 3\). Here, \(3x\) and \(2x\) are like terms as they both represent multiples of \(x\). Similarly, \(7\) and \(3\) are like terms as they're both constants. By adding together those like terms, the simplification of this expression is \(5x + 10\).

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Most popular questions from this chapter

Factor the trinomials , or state that the trinomial is prime. Check your factorization using FOIL multiplication. \(8 x^{2}+33 x+4\)

Factor the trinomials , or state that the trinomial is prime. Check your factorization using FOIL multiplication. \(x^{2}-8 x+32\)

Solve the quadratic equations by factoring. \(5 x^{2}+x=18\)

Factor: \(x^{2 n}+20 x^{n}+99\).

Solve the quadratic equations by factoring. \(x^{2}+7 x=18\)
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