## Thinking Mathematically (6th Edition)

Published by Pearson

# Chapter 6 - Algebra: Equations and Inequalities - 6.1 Algebraic Expressions and Formulas - Exercise Set 6.1 - Page 349: 74

#### Answer

An algebraic expression is the combination of variables and numbers connected with the algebraic operation.

#### Work Step by Step

An algebraic expression is the combination of variables and numbers connected with the algebraic operation (addition, subtraction multiplication, division and power or roots). Examples: (a) $x+y+56$ (b) ${{y}^{2}}+5y+\sqrt{y}$ An algebraic expression contains terms, coefficient, factors, like terms, constant etc. Consider an example of an algebraic expression, (1) $9{{x}^{2}}+5y+2{{x}^{2}}+4$ The terms of an algebraic are those parts that are connected by addition. In the above algebraic expression $9{{x}^{2}},5y,2{{x}^{2}},4$are terms. The numerical value that multiplied with the variable is called the coefficient. In the above algebraic expression $9,5,2$ are the coefficient of ${{x}^{2}},y,{{x}^{2}}$ respectively. Factor of an expression includes every variable, their product and the number that divide the expression completely. In the above algebraic expression, the factor of the term $9{{x}^{2}}$are $x,{{x}^{2}},9,9x,9{{x}^{2}}$. Like terms are the expression that contain same variable and have same power. In the above algebraic expression, $9{{x}^{2}}$ and $2{{x}^{2}}$are the like terms.

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