# simplifying algebraic expressions examples

move the + or â attached in front of them). Simplification of an algebraic expression can be defined as the process of writing an expression in the most efficient and compact form without affecting the value of the original expression. Each line gives a form of the expression, and the rule or rules used to derive it from the previous one. Step 2: Cancel to write in lowest terms. For example, 10x + 63 and 5x – 3 are examples of algebraic expressions. Simplify `(3+1/x)/(5/x+4)` Answer What is a variable? 5y does not have a like term because no other term has the variable y. A term is a constant or the product of a constant and one or more variables. I can't cancel off, say, the a 's, because that a 4 isn't really on top. a) (x + 2)/ (x 2 + 5x + 6) b) (x 2 + 2x - 15)/ (x 2 + x - 12) Show Video Lesson. Simplify an Algebraic Expression by Combining Like Terms. Includes worked examples of fractional exponent expressions. = 3x â 4x + 2a In our example, our simplified terms are 6x and -2, so our new expression is 6x - 2. Then perform the subtraction on the x term: Next, we need to rearrange the expression to put the y terms together. (i) 3xy­­ 3 + 9x 2 y 3 + 5y 3 x (ii) 7ab 2 c 2 + 2a 3 b 2 − 3abc – 5ab 2 c 2 – 2b 2 a 3 + 2ab (iii) 50x 3 – 20x + 8x + 21x 3 – 3x + 15x – 41x 3. Like terms can be added or subtracted from one another. For example, the reciprocal of 5 is `1/5` and the reciprocal of `1 2/3` is `3/5`. b) 10x5 + 3(2x5 - 4b2). Example 1. The twist now is that you are looking for factors that are common to both the numerator and the denominator of the rational expression. The following diagram shows some examples of like terms. First of all, we will rearrange the expression to put the x terms together. b) 5y â 13y Examples Try the free Mathway calculator and To divide by a fraction, you multiply by the reciprocal of the fraction. Before I can cancel anything off, I need to simplify that top parentheses, because it has a negative exponent on it. Algebraic Expressions We welcome your feedback, comments and questions about this site or page. c) p â 3p = (1 â 3)p = â 2p. This site uses cookies, including third-party cookies, to deliver its services, to personalize ads and to analyze traffic. Examples: Simplify. 4 In order to learn the process of simplifying algebraic expressions, you need examples showing you how to combine like terms. Simplify the expressions: Starting with the highest power of x, we see that there are four x-squareds in all (1x 2 + 3x 2). The value of an algebraic expression changes according to the value chosen for the variables of the expressions. Simplifying rational expressions requires good factoring skills. problem and check your answer with the step-by-step explanations. Luckily, many polynomials can be simplified using polynomial factorization. Solution: Creating a table to find the solution: When you combine like terms on “simplifying expressions” problems on your algebra test, you usually have to add or subtract. = 3xâ 2x + 2y + 6 Example 1. Algebraic expressions are made up of terms. You may want to study the “simplifying algebraic expressions examples” in the next section before attempting the quiz below. Simplify all expressions with exponents. You will have several problems on simplifying expressions on your algebra test. Demonstrates how to simplify exponent expressions. So for example, if I have a⁸/a⁵ ... You’ll be using the canceling technique lots in simplifying algebraic expressions, so this is a great opportunity to learn about it early on! If you feel that need further practice with simplifying expressions, please see the following posts before you try the exercises in the next section: Copyright © 2015-2020. Example 2. Putting this all together we get. 2. Expanding an algebraic expression allows you to change the form of an expression without changing the output values it gives. In our previous step, we had the result of 3x + 5y + 6. b) 5y â 13y = (5 â13)y = â8y Relationship between simplifying numerical expressions and simplifying algebraic expressions Try to simplify v + v + v + v + v + v Well, in the same manner, just count how many vs there are and multiply the amount by v. Since there are 6 of them, v + v + v + v + v + v = 6 × v. 2xy does not have a like term because no other term has the variables x and y. Ok, enough vocabulary... let's look at a few examples. Related Pages Please submit your feedback or enquiries via our Feedback page. Numeric expressions apply operations to numbers. For example, `3/4 -: 7/x=3/4xxx/7=(3x)/28` Example 4. To simplify this expression, you remove the parentheses by multiplying 5x by each of the three terms inside the parentheses: = 10x 3 – 15x 2 + 35x. The constant that multiplies the variable (s) in a term is called the coefficient. 3x + 2y â 2x + 6 So, in order to simplify, you need to perform any mathematical operations that you can in the expression.