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, -2ba² and 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

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