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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

4x+7y=29,x+3y=11 substitute method of linear equation
Srinu Reply
substitute method of linear equation
Srinu
Solve one equation for one variable. Using the 2nd equation, x=11-3y. Substitute that for x in first equation. this will find y. then use the value for y to find the value for x.
bruce
I want to learn
Elizebeth
help
Elizebeth
I want to learn. Please teach me?
Wayne
1) Use any equation, and solve for any of the variables. Since the coefficient of x (the number in front of the x) in the second equation is 1 (it actually isn't shown, but 1 * x = x), use that equation. Subtract 3y from both sides (this isolates the x on the left side of the equal sign).
bruce
2) This results in x=11-3y. x is note in terms of y. Use that as the value of x and substitute for all x in the first equation. The first equation becomes 4(11-3y)+7y =29. Note that the only variable left in the first equation is the y. If you have multiple variable, then something is wrong.
bruce
3) Distribute (multiply) the 4 across 11-3y to get 44-12y. Add this to the 7y. So, the equation is now 44-5y=29.
bruce
4) Solve 44-5y=29 for y. Isolate the y by subtracting 44 from birth sides, resulting in -5y=-15. Now, divide birth sides by -5 (since you have -5y). This results in y=3. You now have the value of one variable.
bruce
5) The last step is to take the value of y from Step 4) and substitute into the 2nd equation. Therefore: x+3y=11 becomes x+3(3)=11. Then multiplying, x+9=11. Finally, solve for x by subtracting 9 from both sides. Therefore, x=2.
bruce
6) The ordered pair of (2, 3) is the proposed solution. To check, substitute those values into either equation. If the result is true, then the solution is correct. 4(2)+7(3)=8+21=29. TRUE! Finished.
bruce
At 1:30 Marlon left his house to go to the beach, a distance of 5.625 miles. He rose his skateboard until 2:15, and then walked the rest of the way. He arrived at the beach at 3:00. Marlon's speed on his skateboard is 1.5 times his walking speed. Find his speed when skateboarding and when walking.
Andrew Reply
divide 3x⁴-4x³-3x-1 by x-3
Ritik Reply
how to multiply the monomial
Ceny Reply
Two sisters like to compete on their bike rides. Tamara can go 4 mph faster than her sister, Samantha. If it takes Samantha 1 hours longer than Tamara to go 80 miles, how fast can Samantha ride her bike? Got questions? Get instant answers now!
Seera Reply
how do u solve that question
Seera
Two sisters like to compete on their bike rides. Tamara can go 4 mph faster than her sister, Samantha. If it takes Samantha 1 hours longer than Tamara to go 80 miles, how fast can Samantha ride her bike?
Seera
Speed=distance ÷ time
Tremayne
x-3y =1; 3x-2y+4=0 graph
Juned Reply
Brandon has a cup of quarters and dimes with a total of 5.55$. The number of quarters is five less than three times the number of dimes
ashley Reply
app is wrong how can 350 be divisible by 3.
Raheem Reply
June needs 48 gallons of punch for a party and has two different coolers to carry it in. The bigger cooler is five times as large as the smaller cooler. How many gallons can each cooler hold?
Susanna Reply
Susanna if the first cooler holds five times the gallons then the other cooler. The big cooler holda 40 gallons and the 2nd will hold 8 gallons is that correct?
Georgie
@Susanna that person is correct if you divide 40 by 8 you can see it's 5 it's simple
Ashley
@Geogie my bad that was meant for u
Ashley
Hi everyone, I'm glad to be connected with you all. from France.
Lorris Reply
I'm getting "math processing error" on math problems. Anyone know why?
Ray Reply
Can you all help me I don't get any of this
Jade Reply
4^×=9
Alberto Reply
Did anyone else have trouble getting in quiz link for linear inequalities?
Sireka Reply
operation of trinomial
Justin 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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