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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

In 10 years, the population of Detroit fell from 950,000 to about 712,500. Find the percent decrease.
Jenise Reply
how do i set this up
Jenise
25%
Melissa
25 percent
Muzamil
950,000 - 712,500 = 237,500. 237,500 / 950,000 = .25 = 25%
Melissa
I've tried several times it won't let me post the breakdown of how you get 25%.
Melissa
Subtract one from the other to get the difference. Then take that difference and divided by 950000 and you will get .25 aka 25%
Melissa
Finally 👍
Melissa
one way is to set as ratio: 100%/950000 = x% / 712500, which yields that 712500 is 75% of the initial 950000. therefore, the decrease is 25%.
bruce
twenty five percent...
Jeorge
thanks melissa
Jeorge
950000-713500 *100 and then divide by 950000 = 25
Muzamil
Jeannette has $5 and $10 bills in her wallet. The number of fives is three more than six times the number of tens. Let t represent the number of tens. Write an expression for the number of fives.
jamie Reply
6t+3
Melissa
6t +3
Bollywood
Tricia got a 6% raise on her weekly salary. The raise was $30 per week. What was her original salary?
Iris Reply
let us suppose her original salary is 'm'. so, according to the given condition, m*(6/100)=30 m= (30*100)/6 m= 500 hence, her original salary is $500.
Simply
28.50
Toi
thanks
Jeorge
How many pounds of nuts selling for $6 per pound and raisins selling for $3 per pound should Kurt combine to obtain 120 pounds of trail mix that cost him $5 per pound?
Valeria Reply
Amber wants to put tiles on the backsplash of her kitchen counters. She will need 36 square feet of tiles. She will use basic tiles that cost $8 per square foot and decorator tiles that code $20 per square foot. How many square feet of each tile should she use so that the overal cost of he backsplash will be $10 per square foot?
Nia Reply
I need help with maths can someone help me plz.. is there a wats app group?
Cindy Reply
WY need
Fernando
How did you get $750?
Laura Reply
if y= 2x+sinx what is dy÷dx
formon25 Reply
does it teach you how to do algebra if you don't know how
Kate Reply
Liam borrowed a total of $35,000 to pay for college. He pays his parents 3% interest on the $8,000 he borrowed from them and pays the bank 6.8% on the rest. What average interest rate does he pay on the total $35,000? (Round your answer to the nearest tenth of a percent.)
Lara Reply
exact definition of length by bilbao
francemichael Reply
the definition of length
francemichael Reply
literal meaning of length
francemichael
exact meaning of length
francemichael
exact meaning of length
francemichael
how many typos can we find...?
Chris Reply
5
Joseph
In the LCM Prime Factors exercises, the LCM of 28 and 40 is 280. Not 420!
Chris Reply
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

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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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