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Evaluate 3 x 2 + 4 x + 1 when x = 3 .

40

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Evaluate 6 x 2 4 x 7 when x = 2 .

9

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Indentify and combine like terms

Algebraic expressions are made up of terms. A term is a constant, or the product of a constant and one or more variables.

Term

A term    is a constant, or the product of a constant and one or more variables.

Examples of terms are 7 , y , 5 x 2 , 9 a , and b 5 .

The constant that multiplies the variable is called the coefficient .

Coefficient

The coefficient    of a term is the constant that multiplies the variable in a term.

Think of the coefficient as the number in front of the variable. The coefficient of the term 3 x is 3. When we write x , the coefficient is 1, since x = 1 · x .

Identify the coefficient of each term: 14 y 15 x 2 a .

Solution

The coefficient of 14 y is 14.

The coefficient of 15 x 2 is 15.

The coefficient of a is 1 since a = 1 a .

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Identify the coefficient of each term: 17 x 41 b 2 z .

14 41 1

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Identify the coefficient of each term: 9 p 13 a 3 y 3 .

9 13 1

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Some terms share common traits. Look at the following 6 terms. Which ones seem to have traits in common?

5 x 7 n 2 4 3 x 9 n 2

The 7 and the 4 are both constant terms.

The 5x and the 3 x are both terms with x .

The n 2 and the 9 n 2 are both terms with n 2 .

When two terms are constants or have the same variable and exponent, we say they are like terms .

  • 7 and 4 are like terms.
  • 5 x and 3 x are like terms.
  • x 2 and 9 x 2 are like terms.

Like terms

Terms that are either constants or have the same variables raised to the same powers are called like terms    .

Identify the like terms: y 3 , 7 x 2 , 14, 23, 4 y 3 , 9 x , 5 x 2 .

Solution

y 3 and 4 y 3 are like terms because both have y 3 ; the variable and the exponent match.

7 x 2 and 5 x 2 are like terms because both have x 2 ; the variable and the exponent match.

14 and 23 are like terms because both are constants.

There is no other term like 9 x .

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Identify the like terms: 9 , 2 x 3 , y 2 , 8 x 3 , 15 , 9 y , 11 y 2 .

9 and 15, y 2 and 11 y 2 , 2 x 3 and 8 x 3

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Identify the like terms: 4 x 3 , 8 x 2 , 19, 3 x 2 , 24, 6 x 3 .

19 and 24, 8 x 2 and 3 x 2 , 4 x 3 and 6 x 3

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Adding or subtracting terms forms an expression. In the expression 2 x 2 + 3 x + 8 , from [link] , the three terms are 2 x 2 , 3 x , and 8.

Identify the terms in each expression.

  1. 9 x 2 + 7 x + 12
  2. 8 x + 3 y

Solution

The terms of 9 x 2 + 7 x + 12 are 9 x 2 , 7 x , and 12.

The terms of 8 x + 3 y are 8 x and 3 y .

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Identify the terms in the expression 4 x 2 + 5 x + 17 .

4 x 2 , 5 x , 17

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Identify the terms in the expression 5 x + 2 y .

5 x , 2 y

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If there are like terms in an expression, you can simplify the expression by combining the like terms. What do you think 4 x + 7 x + x would simplify to? If you thought 12 x , you would be right!

4 x + 7 x + x x + x + x + x + x + x + x + x + x + x + x + x 12 x

Add the coefficients and keep the same variable. It doesn’t matter what x is—if you have 4 of something and add 7 more of the same thing and then add 1 more, the result is 12 of them. For example, 4 oranges plus 7 oranges plus 1 orange is 12 oranges. We will discuss the mathematical properties behind this later.

Simplify: 4 x + 7 x + x .

Add the coefficients. 12 x

How to combine like terms

Simplify: 2 x 2 + 3 x + 7 + x 2 + 4 x + 5 .

Solution

Three lines of instructions are listed in a column on the left side of the image while four algebraic expressions are listed on the right. The first line of instruction on the left says: “Step 1. Identify like terms.” Across from step 1 in the right column is the algebraic expression: 2x squared plus 3x plus 7 plus x squared plus 4x plus 5. One line down on the right, the same algebraic expression is repeated, except each of the terms appears in one of three colors to illustrate that these are like terms: 2x squared and x squared appear as red, illustrating that these are like terms; 3x and 4x appear as blue, illustrating that these are also like terms; 7 and 5 appear as green, illustrating that these are like terms as well. The second line of instruction on the left says: “Step 2. Rearrange the expression so the like terms are together. Across from step 2 in the right column is the original algebraic expression with terms reordered so that like terms appear side by side: 2x squared plus x2, both written in red, plus 3x plus 4x, both written n blue, plus 7 plus 5, both written in green. The third line of instruction on the left says: “Step 3. Combine like terms.” Across from step 3 in the right column is the algebraic expression with like terms combined: 3x squared in red, plus 7x in blue, plus 12 in green.
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Simplify: 3 x 2 + 7 x + 9 + 7 x 2 + 9 x + 8 .

10 x 2 + 16 x + 17

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Simplify: 4 y 2 + 5 y + 2 + 8 y 2 + 4 y + 5 .

12 y 2 + 9 y + 7

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Combine like terms.

  1. Identify like terms.
  2. Rearrange the expression so like terms are together.
  3. Add or subtract the coefficients and keep the same variable for each group of like terms.

Questions & Answers

Amara currently sells televisions for company A at a salary of $17,000 plus a $100 commission for each television she sells. Company B offers her a position with a salary of $29,000 plus a $20 commission for each television she sells. How many televisions would Amara need to sell for the options to be equal?
Marisol Reply
what is the quantity and price of the televisions for both options?
karl
I'm mathematics teacher from highly recognized university.
Mzo Reply
is anyone else having issues with the links not doing anything?
Helpful Reply
Yes
Val
chapter 1 foundations 1.2 exercises variables and algebraic symbols
theresa Reply
June needs 45 gallons of punch for a party and has 2 different coolers to carry it in. The bigger cooler is 5 times as large as the smaller cooler. How many gallons can each cooler hold? Enter the answers in decimal form.
Samer Reply
Joseph would like to make 12 pounds of a coffee blend at a cost of $6.25 per pound. He blends Ground Chicory at $4.40 a pound with Jamaican Blue Mountain at $8.84 per pound. How much of each type of coffee should he use?
Samer
4x6.25= $25 coffee blend 4×4.40= $17.60 ground chicory 4x8.84= 35.36 blue mountain. In total they will spend for 12 pounds $77.96 they will spend in total
tyler
DaMarcus and Fabian live 23 miles apart and play soccer at a park between their homes. DaMarcus rode his bike for three-quarters of an hour and Fabian rode his bike for half an hour to get to the park. Fabian’s speed was six miles per hour faster than DaMarcus’ speed. Find the speed of both soccer players.
Sage Reply
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Alvina Reply
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Danteii
help me to understand
Alvina Reply
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Daniel
How many soldiers are there in a group of 27 sailors and soldiers if there are four fifths many sailors as soldiers?
tyler
What is the domain and range of heaviside
Christopher Reply
What is the domain and range of Heaviside and signum
Christopher
25-35
Fazal
The hypotenuse of a right triangle is 10cm long. One of the triangle’s legs is three times the length of the other leg. Find the lengths of the three sides of the triangle.
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Tickets for a show are $70 for adults and $50 for children. For one evening performance, a total of 300 tickets were sold and the receipts totaled $17,200. How many adult tickets and how many child tickets were sold?
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Edi Reply
June needs 45 gallons of punch for a party and has 2 different coolers to carry it in. The bigger cooler is 5 times as large as the smaller cooler. How many gallons can each cooler hold?
Jesus Reply
Washing his dad’s car alone, eight-year-old Levi takes 2.5 hours. If his dad helps him, then it takes 1 hour. How long does it take the Levi’s dad to wash the car by himself?
Ronald Reply
Bruce drives his car for his job. The equation R=0.575m+42 models the relation between the amount in dollars, R, that he is reimbursed and the number of miles, m, he drives in one day. Find the amount Bruce is reimbursed on a day when he drives 220 miles.
Dojzae Reply

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Source:  OpenStax, Elementary algebra. OpenStax CNX. Jan 18, 2017 Download for free at http://cnx.org/content/col12116/1.2
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