{"id":106101,"date":"2021-12-10T07:55:27","date_gmt":"2021-12-10T13:55:27","guid":{"rendered":"https:\/\/www.mometrix.com\/academy\/?page_id=106101"},"modified":"2026-03-28T12:23:42","modified_gmt":"2026-03-28T17:23:42","slug":"evaluating-algebraic-expressions","status":"publish","type":"page","link":"https:\/\/www.mometrix.com\/academy\/evaluating-algebraic-expressions\/","title":{"rendered":"Evaluating Algebraic Expressions Overview"},"content":{"rendered":"

What is an algebraic expression?<\/h2>\n

An algebraic expression is a mathematical phrase that includes variables, constants, coefficients, and algebraic operations. For example, \\(5x^2+6xy-c\\) is an algebraic expression. Unlike algebraic equations, algebraic expressions do not have equal signs.<\/p>\n

Algebraic Expression Sample Questions<\/a><\/div>\n

There are several types of algebraic expressions. A monomial<\/strong> is an algebraic expression with only one term in which the exponents and variables are non-negative integers. A binomial<\/strong> is an algebraic expression composed of two monomials linked by an operation symbol. A trinomial<\/strong> consists of three monomials linked by operation symbols. A polynomial<\/a> is an algebraic expression with any amount of terms greater than 1 but not an infinite amount.<\/p>\n

How do you evaluate algebraic expressions?<\/h2>\n

To evaluate algebraic expressions, substitute each variable\u2019s value into the expression. When substituting a number in for a variable, it is always a good idea to put it in parentheses. This helps you correctly simplify exponents and multiply. Once you\u2019ve done this, simplify using the order of operations<\/a>.<\/p>\n

For instance, to evaluate the expression \\(4s^2-1\\) when \\(s=2\\), substitute the number \\(2\\) into the expression for \\(s\\) and solve:<\/p>\n\n\n\n\n\n\n
\\(4(2)^2-1\\)<\/td>\nFirst, substitute \\(2\\) into the expression for \\(s\\).<\/td>\n<\/tr>\n
\\(4(4)-1\\)<\/td>\nThe expression involves multiplication, an exponent, and subtraction. According to the order of operations, simplify exponents before multiplying or subtracting. Since \\(2\\) raised to the second power equals \\(4\\), rewrite the expression using \\(4\\).<\/td>\n<\/tr>\n
\\(16-1\\)<\/td>\nThe two operations remaining in the expression are multiplication and subtraction. According to the order of operations, multiply before subtracting. Since \\(4\\times4=16\\), rewrite the expression using \\(16\\).<\/td>\n<\/tr>\n
\\(15\\)<\/td>\nFinally, subtract. Since \\(16-1=15\\), the expression \\(4s^2-1\\) is simplified to \\(15\\) when \\(s=2\\).<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Examples<\/h3>\n

1. Evaluate \\(xyz\\) if \\(x=3,y=2,\\) and \\(z=1\\).<\/p>\n\n\n\n\n\n
\\((3)(2)(1)\\)<\/td>\nFirst, substitute \\(3\\) into the expression for \\(x\\), \\(2\\) for \\(y\\), and \\(1\\) for \\(z\\). When \\(2\\) or more variables are adjacent to each other with no operation sign, always multiply. In this case, multiply \\(3\\times2\\times1\\).<\/td>\n<\/tr>\n
\\((6)(1)\\)<\/td>\nMultiply from left to right. Since \\(3\\times2=6\\), rewrite the expression using \\(6\\).<\/td>\n<\/tr>\n
\\(6\\)<\/td>\nFinally, multiply \\((6)(1)\\). Since \\(6\\times1=6\\), the expression \\(xyz\\) is simplified to \\(6\\) when \\(x=3,y=2,\\) and \\(z=1\\).<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

2.Evaluate \\(\\frac{x+(3+y^3)}{10-z}\\) if \\(x=5,y=3,\\) and \\(z=3\\).<\/p>\n\n\n\n\n\n\n\n
\\(\\frac{(5)+(3+(3)^3)}{10-(3)}\\)<\/td>\nFirst, substitute \\(5\\) into the expression for \\(x\\), \\(3\\) for \\(y\\), and \\(3\\) for \\(z\\).<\/td>\n<\/tr>\n
\\(\\frac{(5)+(3+27)}{10 – (3)}\\)<\/td>\nThis expression involves parentheses, exponents, division, addition, and subtraction. Start by addressing the portion of the expression in parentheses, \\((3+(3)^3)\\). According to the order of operations, simplify exponents first. Since \\(3^3\\) is equal to \\(27\\), rewrite the expression using \\(27\\).<\/td>\n<\/tr>\n
\\(\\frac{(5)+(30)}{10 – (3)}\\)<\/td>\nNext, continue to simplify the portion of the expression in parentheses by adding. Since \\(3+27=30\\), rewrite the expression using \\(30\\).<\/td>\n<\/tr>\n
\\(\\frac{35}{7}\\)<\/td>\nFrom here, simplify the numerator and denominator. Since \\(5+30=35\\), write \\(35\\) as the numerator. Since \\(10-3=7\\), write \\(7\\) as the denominator.<\/td>\n<\/tr>\n
\\(5\\)<\/td>\nFinally, simplify the fraction by dividing the numerator by the denominator. Since \\(35\\div7=5\\), the expression \\(\\frac{x+(3+y^3)}{10-z}\\) is simplified to \\(5\\) when \\(x=5,y=3,\\) and \\(z=3\\).<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

3. Evaluate \\(-3a-(2b+4)\\) if \\(a=-8\\) and \\(b=-7\\).<\/p>\n\n\n\n\n\n\n\n
\\(-3(-8)-(2(-7)+4)\\)<\/td>\nFirst, substitute \\(-8\\) into the expression for \\(a\\) and \\(-7\\) for \\(b\\).<\/td>\n<\/tr>\n
\\(-3(-8)-((-14)+4)\\)<\/td>\nThis expression involves parentheses, multiplication, addition, and subtraction. Start by addressing the portion of the expression in parentheses, \\((2(-7)+4)\\). According to the order of operations, simplify \\(2(-7)\\) first. Since \\(2-7=-14\\), rewrite the expression using this product.<\/td>\n<\/tr>\n
\\(-3(-8)-(-10)\\)<\/td>\nNext, continue to simplify the portion of the expression in parentheses by simplifying \\(((-14)+4)\\). Since \\(-14+4=-10\\), rewrite the expression using this sum.<\/td>\n<\/tr>\n
\\(24-(-10)\\)<\/td>\nFrom here, multiply \\(-3(-8)\\). Since \\(-3\\times-8=24\\), rewrite the expression using this product.<\/td>\n<\/tr>\n
\\(34\\)<\/td>\nFinally, subtract \\(24-(-10)\\). Since \\(24-(-10)=34\\), the expression \\(-3a-(2b+4)\\) is simplified to \\(34\\) when \\(a=-8\\) and \\(b=-7\\).<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\"Click<\/a>\n

Evaluating Algebraic Expressions Sample Questions<\/h2>\n

Here are a few sample questions going over evaluating algebraic expressions.
\n\n\t\t\t\t

\n\t\t\t\t\tQuestion #1:<\/strong>\n\t\t\t\t\t

 
\nEvaluate \\(\\frac{ac}{b}\\) if \\(a=5,b=2,\\) and \\(c=10\\). <\/p>\n<\/div>\n\t\t\t\t\t

\\(1\\)<\/div>
\\(5\\)<\/div>
\\(25\\)<\/div>
\\(255\\)<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t