# COMBINING LIKE TERMS WORKSHEET

## About "Combining like terms worksheet"

Combining like terms worksheet is much useful to the kids who would like to practice problems on addition and subtraction of polynomials.

## Combing like terms worksheet - Problems

1)  Add :  3x³  +  x² -  2   and  2x²  + 5x + 5

2)  Find out the sum of the polynomials  3x - y, 2y - 2x,               and x + y.

3)  Subtract 5xy from 8xy.

4)  Subtract (3c + 7d²)  from  (5c - d²)

5)  Subtract ( 2x² + 2y² - 6 )  from  ( 3x² - 7y² + 9 )

6)  Add ( 7p³ +  4p²- 8p + 1 ) and (3p³- 5p²- 10p + 5)

7)  Add ( 2x³ + 5x² - 2x + 7 ) and ( x³ + 4x² - x + 6)

8)  Add ( 3x³ - 2x² - x + 4 ) and ( 2x³ + 7x² - 3x - 3 )

9)  Add 2( x³ - x² + 6x - 2 ) and ( 5x⁶ + 7x⁵ - 3x - 3 )

10)   Add -1( x⁶ + x³ + 6x² - 2 ) and 2( 5x⁶ + 7x⁵ - 3x - 3 )

11)  Add  5( 5x⁶ + 2x³ - 6x² - 2 ) + 6(-3x⁶ + 2x⁵ + 2x + 1 )

12)  Add  -2 ( 2x⁴ - 2x³ - x² + 5 ) and 3 ( 2x⁴ - 2x² - 3 )

13)  Add   5( x⁴ - x³ + 5 ) and  2( x⁴ - 5x² - 7 )

14)  Add  3( 6x⁴ - 2x³ - 3 ) and 2( 2x⁴ - x² - 8 )

15)   Add (6x⁷-2x⁶-3x³+2x²) and 2(2x⁴+5x⁷+ 3x⁶+ x³+x²)

16)  Add (x⁷-3x⁶-2x³+x²) and  5(3x⁴+15x⁷+4x⁶+2x³+6x²)

## Combining like terms worksheet - Answers

Problem 1 :

Add :  3x³  +  x² -  2   and  2x²  + 5x + 5

Solution :

First we have to arrange the like terms column wise and add them. Observe the important points related to the above work.

1. We have written the term 2x² of the second polynomial below the corresponding term x² of the first polynomial. (Because x² and 2x² are like terms and they can be combined)

2. Similarly, the constant term +5 is placed below the constant term – 2.

3. Since the term x in the first polynomial and the term x³ in the second polynomial do not exist, their respective places have been left blank to  facilitate the process of addition.Or, for the non existing terms, we annexe the terms with zero coefficients.

Let us look at the next problem on "Combining like terms worksheet"

Problem 2 :

Find out the sum of the polynomials  3x - y, 2y - 2x, and x + y.

Solution :

We can find out the sum of the given polynomials using either column method of addition or row method of addition as explained below.

Once they are written in the above methods, we have to combine the like terms.  Let us look at the next problem on "Combining like terms worksheet"

Problem 3 :

Subtract 5xy from 8xy.

Solution : Let us look at the next problem on "Combining like terms worksheet"

Problem 4 :

Subtract (3c + 7d²)  from  (5c - d²)

Solution :  Alternatively, this can also be done as :

( 5c - d² ) - ( 3c + 7d² ) =  5c - d²  -  3c - 7d²

=  ( 5c - 3c ) + ( -d² - 7d² )

=  2c  + ( - 8d² )

=  2c   - 8d²

Let us look at the next problem on "Combining like terms worksheet"

Problem 5 :

Subtract ( 2x² + 2y² - 6 )  from  ( 3x² - 7y² + 9 )

Solution :  Let us look at the next problem on "Combining like terms worksheet"

Problem 6 :

Add ( 7p³ +  4p²- 8p + 1 ) and (3p³- 5p²- 10p + 5)

Solution :

Step 1:

The two given polynomials are already in the arranged form.So we can leave it as it is.

=  ( 7p³ + 4p²- 8p + 1) + (3p³ - 5p² - 10p + 5)

Step 2 :

Now we have to write the like terms together starting from the highest power to lowest power.

= 7p³ + 3p³ + 4p²- 5p²- 8p - 10p + 1 + 5 So the final answer is  10p³- 1p²- 18p + 6

Let us look at the next problem on "Combining like terms worksheet"

Problem 7 :

Add ( 2x³ + 5x² - 2x + 7 ) and ( x³ + 4x² - x + 6)

Solution :

=  ( 2x³ + 5x² - 2x + 7 ) + ( x³ + 4x² - x + 6)

=  2x³ + 5x² - 2x + 7 + x³ + 4x² - x + 6

=  2x³ + x³ + 5x² + 4x² - 2x - x + 7 + 6

=  3x³ + 9x² - 3x + 13

Let us look at the next problem on "Combining like terms worksheet"

Problem 8 :

Add ( 3x³ - 2x² - x + 4 ) and ( 2x³ + 7x² - 3x - 3 )

Solution :

=  (3x³ - 2x² - x + 4) + (2x³ + 7x² - 3x - 3)

=  3 x³ - 2 x² - x + 4 + 2 x³ + 7 x² - 3 x - 3

=  3x³ + 2x³ - 2x² + 7x² - x - 3x + 4 - 3

=  5x³ + 5x² - 4x + 1

Let us look at the next problem on "Combining like terms worksheet"

Problem 9 :

Add 2( x³ - x² + 6x - 2 ) and ( 5x⁶ + 7x⁵ - 3x - 3 )

Solution :

=  2( x³ - x² + 6 x - 2 ) + ( 5 x⁶ + 7 x⁵ - 3 x - 3 )

=  2x³ - 2x² + 12x - 4 + 5x⁶ + 7x⁵ - 3x - 3

=  5x⁶ + 7x⁵ + 2x³ - 2x² + 12x - 3x - 4 - 3

=  5x⁶ + 7x⁵ + 2x³ - 2x² + 9x - 7

Let us look at the next problem on "Combining like terms worksheet"

Problem 10 :

Add -1( x⁶ + x³ + 6x² - 2 ) and 2( 5x⁶ + 7x⁵ - 3x - 3 )

Solution :

=  -1( x⁶ + x³ + 6x² - 2 ) + 2( 5x⁶ + 7x⁵ - 3x - 3 )

=  -x⁶ - x³ - 6x² + 2 + 10x⁶ + 14x⁵ - 6x - 6

=  -x⁶ + 10x⁶ + 14x⁵ - x³ - 6x² - 6x + 2 - 6

=  9x⁶ + 14x⁵ - x³ - 6x² - 6x - 4

Let us look at the next problem on "Combining like terms worksheet"

Problem 11 :

Add  5( 5x⁶ + 2x³ - 6x² - 2 ) + 6(-3x⁶ + 2x⁵ + 2x + 1 )

Solution :

=  5( 5x⁶ + 2x³ - 6x² - 2 ) + 6( -3x⁶ + 2x⁵ + 2x + 1 )

=  25x⁶ + 10x³ - 30x² - 10 -18x⁶ + 12x⁵ + 12x + 6

=  25x⁶ -18x⁶ + 12x⁵ + 10x³ - 30x² + 12x -10 + 6

=  7x⁶ + 12x⁵ + 10x³ - 30x² + 12x - 4

Let us look at the next problem on "Combining like terms worksheet"

Problem 12 :

Add  -2 ( 2x⁴ - 2x³ - x² + 5 ) and 3 ( 2x⁴ - 2x² - 3 )

Solution :

=  -2( 2x⁴ - 2x³ - x² + 5 ) +  3( 2x⁴ - 2x² - 3 )

=  -4x⁴ + 4x³ + 2x² -10 +  6x⁴ - 6x² - 9

=  -4x⁴ + 6x⁴ + 4x³ + 2x² - 6x² -10 - 9

=  2x⁴ + 4x³ - 4x² - 19

Let us look at the next problem on "Combining like terms worksheet"

Problem 13 :

Add   5( x⁴ - x³ + 5 ) and  2( x⁴ - 5x² - 7 )

Solution :

= 5( x⁴ - x³ + 5 ) +  2( x⁴ - 5x² - 7 )

= 5x⁴ - 5 x³ + 25 + 2x⁴ - 10x² - 14

= 5x⁴ + 2x⁴ - 5x³ - 10x² + 25 - 14

= 7x⁴ - 15x³ + 11

Let us look at the next problem on "Combining like terms worksheet"

Problem 14 :

Add  3( 6x⁴ - 2x³ - 3 ) and 2( 2x⁴ - x² - 8 )

Solution :

=  3 ( 6x⁴ - 2x³ - 3 ) +  2 ( 2x⁴ - x² - 8 )

= 18x⁴ - 6x³ - 9 + 4x⁴ -2x² - 16

= 18x⁴ + 4x⁴ - 6x³ -2x² - 9 - 16

= 22 x⁴ - 6x³ -2x² - 25

Let us look at the next problem on "Combining like terms worksheet"

Problem 15 :

Add (6x⁷-2x⁶-3x³+2x²) and 2(2x⁴+5x⁷+ 3x⁶+ x³+x²)

Solution :

= ( 6x⁷- 2x⁶- 3x³+ 2x²) + 2( 2x⁴ + 5x⁷ + 3x⁶ + x³ + x² )

= 6x⁷ - 2x⁶ - 3x³ + 2x² + 4x⁴ + 10x⁷ + 6x⁶ + 2x³ + 2x²

= 6x⁷ + 10x⁷- 2x⁶ + 6x⁶ + 4x⁴ - 3x³ + 2x³ + 2x² + 2x²

= 16x⁷ + 4x⁶ + 4x⁴ - x³ + 4x²

Let us look at the next problem on "Combining like terms worksheet"

Problem 16 :

Add (x⁷-3x⁶-2x³+x²) and 5 (3x⁴+15x⁷+4x⁶+2x³+6x²)

Solution :

=  (x⁷-3x⁶-2x³+x²) + 5 (3x⁴ + 15x⁷ + 4x⁶ + 2x³+ 6x² )

= x⁷- 3x⁶ - 2x³ + x² + 15x⁴ + 75x⁷ + 20x⁶ + 10x³ + 30x²

= x⁷ + 75x⁷- 3x⁶ + 20x⁶ - 2x³ + 10x³ + x² + 30x²

= 76x⁷ + 17x⁶ + 8x³ + 31x²

After having gone through the stuff and example problems, we hope that the students would have understood "How to combine like terms".

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