Worksheet on Combining Like Terms

Practice the questions given in the worksheet on combining like terms and unlike terms. The questions are based on grouping and combining the like terms with addition & subtraction and problems on adding or subtracting terms that involves variables by combining like and unlike terms.

1. Find the sum of combining like terms:

(i) a + 2b – 3c; -3a + b +2c and 2a – 3b + c

(ii) -3x + 2y + z; x – 3y + 2z and 2x + y – 3z

(iii) 4p + 3q + 5r; -2p + 3q – 8r and p – q + r

(iv) a + b + c; 2a + 3b – 2c and 3a – 4b + c

(v) -17q – 2r + 23p; -9p + 15q + 7r and -13p + 3q – 4r

2. Subtract from:

(i) 3ab – 5bc + 8ca take -4ab + 2bc – 10ca

(ii) 4m² – 3m + 2 take -5m² + 6m – 7

(iii) x²yz + y²zx + z²xy take 3x²yz – 5y²zx – 4z²xy

(iv) bc – ca + ab take –ab + bc – ca

(v) -2a³ – a² – 3a + 2 take a³ – a + 1

Now we will practice the word problems on addition and subtraction combining like terms provided in the worksheet on combining like terms.

3. To the sum of 2x – 3y - 2z and 2y – x + 7z at the sum of x – 4z + 7y and z – 6y.

4. Subtract 3m – 7m³ + 5m² from the sum of 2 + 8m² – m³ and 2m³ – 3m² + m – 2.

5. What should be added to a³ – 4a²b + 3ab² – 2b³ to get 3a³ + a²b – 2ab² – 6b³?

6. What should be added to 3p³ – 5p² + 9p – 11 to get 0?

7. What should be subtracted from m³ – 3m²n – 5m² + 9 to get 0?

8. The sum of the two algebraic expressions is p – 2q + 3r. If one of them is 3p – q – 2r, find the other.

9. From the sum of x + y – z and 2x – 5y + 3z, subtract the sum of 4x – y + z and x – y – 4z

10. By how much does 2z³ – 4z² + z – 1 exceeded z³ – 2z² + z + 1.

11. If the perimeter of a triangle is 2a + 17b + 6c and the two sides are 4a – 3b + 5c, 3a + 7b – 2c, find the third side.

12. The two sides of a rectangle are 2p³ – 3q³ + 2r³ and -5p³ + 2q³ – 2r³. Find its perimeter.

Answers for the worksheet on combining like terms are given below to check the exact answers of the above problems.

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Answers:

1. (i) 0

(ii) 0

(iii) 3p + 5q - 2r

(iv) 6a

(v) p + q + r

2. (i) 7ab – 7bc + 18ca

(ii) 9m² – 9m + 9

(iii) -2x²yz + 6y²zx + 5z²xy

(iv) 2ab

(v) -3a³ – a² – 2a + 1



3. 2x + 2z

4. 8m³ – 2m

5. 2a³ + 5a²b - 5ab² – 4b³

6. -3p³ + 5p² - 9p + 11

7. m³ – 3m²n – 5mn² + 9

8. -2p – q + 5r

9. -2x - 2y + 5z

10. z³ – 2z² - 2

11. -5a + 13b + 3c

12. 14p³ – 2q³

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