Worksheet on Addition and Subtraction of Polynomials

Practice the problems given in the worksheet on addition and subtraction of polynomials. The questions are based on word problems on adding and subtracting polynomials.

1. Solve the following polynomials:

(i)Take –pq + qr – rp from qr – rp + pq

(ii) Take 5a + 6b – 3c from 3a + 5b – 4c

2. (i) How much is -3k less than 3k?

(ii) How much is 2a + b greater than a – 2b?

(iii) What should be added to 2p – q + r to make it p + q – 2r?

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

4. Subtract a – 2b – c from the sum of 3a – b + c and a + b – 3c.

5. How much should a + 2b – 3c be increased to get 3a?

6. The sum of two expressions is 3x² + 2xy – y². If one of them is 2x² + 3y², find the other.

7. From the sum of 4b² + 5bc, -2b² – 2bc – 2z² and 2bc + 4c², subtract the sum of 5b² – c² and -3b² + 2bc + c².

8. What should be subtracted from 3x + 5y + 9 to get - 2x + 3y + 15?

9. What should be taken away from p² – q² + 2pq + 10 to obtain – 2p² – 2q² + 7pq + 10?

10. By how much must 5p² – 3q² be diminished to give 2p² + q²?

11. Subtract 2m – 5q + 7 from 4p + 2q and add your result to m² – 3m³ + m - 1.

12. Subtract 2a²b – 3b² from 3a² – 5ab² + 2b² and subtract your result from the sum of the two expressions 3ab² + 5b² – 2a²b and a²b + 5a² – 3ab².

Answers for the worksheet on addition and subtraction of polynomials are given below to check the exact answers of the above word problems.

Answers:

1. (i) 2pq

(ii) -2a – b - c

2. (i) 6k

(ii) a + 3b

(iii) -p + 2q – 3r

3. 2x + 2y + 3z

4. 3a + 2b - c

5. 2a – 2b + 3c

6. x² + 2xy – 4y²

7. 3bc + 2c²

8. 5x + 2y - 6

9. 3p² + q² – 5pq

10. 3p² – 4q²

11. 4p + 7q – m + m² – 3m³ - 8

12. 2a² + a²b + 5ab²

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