Worksheet on Addition of Polynomials

Practice the questions given in the worksheet on addition of polynomials. The questions are based on arranging the expressions to find the sum of monomials, binomials, trinomials and polynomials.

1. Arrange and add the monomials:

(i) –8abc and 10abc

(ii) 5x²yz² and 9x²yz²

(iii) -6z⁷, and 5z⁷

2. Arrange and add the binomials:

(i) 2p + 3q and 7p + 8q

(ii) 14x -3y and -5x + 11y

(iii) 2x²y and -8x²y

3. Arrange and add the trinomials:

(i) 4x + 5y – 3z and 9x – 6y + 4z

(ii)3x² + 4xy + 5y² and 9y² – 10x² – 6xy

(iii) 14xy + 17yz + 13xz and 8xy – 15yz + 12xz

Now we will proceed from basic to intricate problems on arranging and adding polynomials provided in the worksheet on addition of polynomials.

4. Find the sum of:

(i) 3x² – 2xy + 4y² and – x² + 4xy – 2y²

(ii) 3p + 4q + 7r, -5p + 3q – 6r and 4p – 2q – 4r

(iii) 2a² + ab - b², -a² + 2ab + 3b² and 3a² – 10ab + 4b²

(iv) k² – k + 1, -5k² + 2k – 2 and 3k² – 3k + 1

(v) x² – xy + yz, 2xy + yz – 2x² and -3yz + 3x² + xy

(vi) 4u² + 7 – 3u, 4u – u² + 8 and -10 + 5u – 2u²

5. Add the following expressions:

(i) 3xyz + 4yz + 5zx, 7xz – 6yz + 4xyz and -9xyz – 11zy + 9xz

(ii) x³ – 2y³ + x, y³ – 2x³ + y and -2y + 2y³ – 5x + 4x³

(iii) 7p² – 4p²q + 8q², 5q² – 2p² + 6p²q and 3p²q + 10p²

(iv) 9x² – 7x + 5, -14x² – 6 + 15x and 20x² + 40x - 17

(v) –m² – 3mn + 3n² + 8, 3m² – 5n² – 3 + 4mn and -6mn + 2m² – 2 + n²

6. If P = a² – 2bc + b², Q = -b² + bc – c² and R = c² + cb + a² then, find the value of P + Q + R.

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

Answers:

1. (i) 2abc

(ii) 14x²yz²

(iii) -z⁷

2. (i) 9p + 11q

(ii) 9x + 8y

(iii) -6x²y

3. (i) 13x - y +z

(ii) -7x² - 2xy + 14y²

(iii) 22xy + 2yz + 25xz

4. (i) 2x² + 2xy + 2y²

(ii) 2p + 5q – 3r

(iii) 4a² – 7ab + 6b²

(iv) –k² – 2k

(v) 2x² + 2xy - yz

(vi) u² + 6u + 5

5. (i) -2xyz – 13yz + 21xz

(ii) 3x³ + y³ – 4x – y

(iii) 15p² + 5p²q + 13q²

(iv) 15x² – 32x – 18

(v) 4m² – 5mn – n²

6. 0

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