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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

Aziza is solving this equation-2(1+x)=4x+10
Sechabe Reply
No. 3^32 -1 has exactly two divisors greater than 75 and less than 85 what is their product?
KAJAL Reply
x^2+7x-19=0 has Two solutions A and B give your answer to 3 decimal places
Adedamola Reply
please the answer to the example exercise
Patricia Reply
3. When Jenna spent 10 minutes on the elliptical trainer and then did circuit training for20 minutes, her fitness app says she burned 278 calories. When she spent 20 minutes onthe elliptical trainer and 30 minutes circuit training she burned 473 calories. How manycalories does she burn for each minute on the elliptical trainer? How many calories doesshe burn for each minute of circuit training?
Edwin Reply
.473
Angelita
?
Angelita
John left his house in Irvine at 8:35 am to drive to a meeting in Los Angeles, 45 miles away. He arrived at the meeting at 9:50. At 3:30 pm, he left the meeting and drove home. He arrived home at 5:18.
DaYoungan Reply
p-2/3=5/6 how do I solve it with explanation pls
Adedamola Reply
P=3/2
Vanarith
1/2p2-2/3p=5p/6
James
don't understand answer
Cindy
4.5
Ruth
is y=7/5 a solution of 5y+3=10y-4
Adedamola Reply
yes
James
don't understand answer
Cindy
Lucinda has a pocketful of dimes and quarters with a value of $6.20. The number of dimes is 18 more than 3 times the number of quarters. How many dimes and how many quarters does Lucinda have?
Rhonda Reply
Find an equation for the line that passes through the point P ( 0 , − 4 ) and has a slope 8/9 .
Gabriel Reply
is that a negative 4 or positive 4?
Felix
y = mx + b
Felix
if negative -4, then -4=8/9(0) + b
Felix
-4=b
Felix
if positive 4, then 4=b
Felix
then plug in y=8/9x - 4 or y=8/9x+4
Felix
Macario is making 12 pounds of nut mixture with macadamia nuts and almonds. macadamia nuts cost $9 per pound and almonds cost $5.25 per pound. how many pounds of macadamia nuts and how many pounds of almonds should macario use for the mixture to cost $6.50 per pound to make?
Cherry Reply
Nga and Lauren bought a chest at a flea market for $50. They re-finished it and then added a 350 % mark - up
Makaila Reply
$1750
Cindy
the sum of two Numbers is 19 and their difference is 15
Abdulai Reply
2, 17
Jose
interesting
saw
4,2
Cindy
Felecia left her home to visit her daughter, driving 45mph. Her husband waited for the dog sitter to arrive and left home 20 minutes, or 13 hour later. He drove 55mph to catch up to Felecia. How long before he reaches her?
Rafi Reply
hola saben como aser un valor de la expresión
NAILEA
integer greater than 2 and less than 12
Emily Reply
2 < x < 12
Felix
I'm guessing you are doing inequalities...
Felix
Actually, translating words into algebraic expressions / equations...
Felix
hi
Darianna
hello
Mister
Eric here
Eric
6
Cindy

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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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