# LIKE TERMS AND UNLIKE TERMS WORKSHEET

Problem 1 :

Group the like terms together :

x2, -2x, 2x2, 5x, 3x2/2 and -5x

Problem 2 :

Group the like terms together :

3x, -y, 2y, -2x, x and y

Problem 3 :

List out the like terms :

5m3n2, 7m2n3, -3m3n2, 4mn3 and 7m3n2

Problem 4 :

List out the like terms :

15a2b, 5ab2, -2ba2, 3a2b

Problem 5 :

Are the two terms given below like terms ? Explain.

3a2bc3, and -5ba2c3

Problem 6 :

Are the two terms given below like terms ? Explain.

3x3yz3, and -5yx3z2

Problem 7 :

Add :

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

Problem 8 :

Add :

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

Problem 9 :

Add :

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

Problem 10 :

Add :

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

Problem 11 :

Add :

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

Problem 12 :

Add :

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

Problem 13 :

Add :

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

Problem 14 :

Add :

5(x4 - x3 + 5) and  2(x4 - 5x2 - 7)

Problem 15 :

Add :

(6x7 - 2x6 - 3x3 + 2x2) and 2(2x4 + 5x7 + 3x6 + x3 + x2) ## Detailed Answer Key

Problem 1 :

Group the like terms together :

x2, -2x, 2x2, 5x, 3x2/2 and -5x

Solution :

(x2,  2x2, 3x2/2) and (-2x, 5x, -5x)

Problem 2 :

Group the like terms together :

3x, -y, 2y, -2x, x and y

Solution :

(3x,  -2x, x) and (-y, 2y, y)

Problem 3 :

List out the like terms :

5m3n2, 7m2n3, -3m3n2, 4mn3 and 7m3n2

Solution :

5m3n2, -3m3n2 and 7m3n2

Problem 4 :

List out the like terms :

15a2b, 5ab2, -2ba2, 3a2b

Solution :

15a2b, -2baand 3a2b

Problem 5 :

Are the two terms given below like terms ? Explain.

3a2bc3, and -5ba2c3

Solution :

Yes, the above two terms are like terms.

Because, both the terms are having the same variables with same exponent.

Problem 6 :

Are the two terms given below like terms ? Explain.

3x3yz3, and -5yx3z2

Solution :

Even though both the terms are having the same variables x, y and z, one of the variables (z) does not have the same exponent.

In the first term, z has the exponent 3 and in the second term, z has the exponent 2.

So, the above two terms are not like terms.

They are unlike terms.

Problem 7 :

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 ) and (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.

Problem 8 :

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

Problem 9 :

Add :

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

Solution :

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

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

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

=  5x3 + 5x2 - 4x + 1

Problem 10 :

Add :

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

Solution :

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

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

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

=  5x6 + 7x6 + 2x3 - 2x2 + 9x - 7

Problem 11 :

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

Problem 12 :

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

Problem 13 :

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

Problem 14 :

Add :

5(x4 - x3 + 5) and  2(x4 - 5x2 - 7)

Solution :

=  5(x4 - x3 + 5) +  2(x4 - 5x2 - 7)

=  5x4 - 5x3 + 25 + 2x4 - 10x2 - 14

=  5x4 + 2x4 - 5x3 - 10x2 + 25 - 14

=  7x4 - 5x3 - 10x2 + 11

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 Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here.

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