# 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.

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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