Adding Polynomials Worksheet includes questions on finding the degree of the polynomial, identifying kind of polynomials, adding given monomials, binomials, trinomials, etc. The Addition of the Polynomials Worksheet gives you engagement and abundant practice on theories around polynomials.

Step by Step Method used for explaining the problems in the Worksheet on Addition of Polynomials will strengthen your algebraic skills as well as helps you get grip on the concept. Make the most out of the handy Addition of Polynomials Worksheet PDF in Printable Format over here and practice anytime and anywhere.

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## Addition of Polynomials Worksheet PDF

**I.** **Arrange and add the monomials
**(i) –6xyz and 8xyz

(ii) 5a

^{2}b

^{2}and 9a

^{2}b

^{2}

(iii) 5a

^{5}, and -3a

^{5}

**Solution:**

(i) Given monomials are –6xyz and 8xyz

=(-6xyz)+(8xyz)

=-6xyz+8xyz

=2xyz

Hence, By adding –6xyz and 8xyz we get 2xyz.

(ii) Given monomials are 5a^{2}b^{2} and 9a^{2}b^{2}

=5a^{2}b^{2} + 9a^{2}b^{2}

= 14 a^{2}b^{2}

Hence, By adding 5a^{2}b^{2} and 9a^{2}b^{2} we get 14 a^{2}b^{2} .

(iii) Given monomials are 5a^{5}, and -3a^{5
}=5a^{5}+(-3a^{5})

=5a^{5}-3a^{5}

=2a^{ 5}

Hence, By adding 5a^{5} and -3a^{5} we get 2a^{ 5}.

**II.** **Arrange and add the binomials:
**(i) 6m + 8n and 4m + 2n

(ii) 17a -5b and -3a+ 15b

(iii) 4a

^{2}b + 2b and -10a

^{2}b + 5b

**Solution:**

(i) Given binomials are 6m + 8n and 4m + 2n

Arrange the like terms and then add,

=6m+4m+8n+2n

=10m+10n

Hence, By adding the binomials 6m + 8n and 4m + 2n we get 10m+10n.

(ii) Given binomials are 17a -5b and -3a+ 15b

Arrange the like terms and then add,

=17a-3a-5b+15b

=14a+10b

(iii) Given binomials are 4a^{2}b + 2b and -10a^{2}b + 5b

Arrange the like terms and then add,

=4a^{2}b -10a^{2}b + 2b + 5b

=-6a^{2}b+7b

**III. Arrange and add the trinomials:
**(i) 3x + 2y – z and 14x – 7y + 2z

(ii) 5a

^{2}+ 3ab + 2b

^{2}and 10a

^{2}– 8b

^{2}– 5ab

(iii) 18mn + 10np + 15mp and 10mn – 13np + 14mp

**Solution:**

(i) Given trinomials are 3x + 2y – z and 14x – 7y + 2z

Arrange the like terms and then add,

=3x+14x+2y-7y-z+2z

=17x-5y+z

Hence, By adding the trinomials 3x + 2y – z and 14x – 7y + 2z we get 17x-5y+z.

(ii) Given trinomials are 5a^{2} + 3ab + 2b^{2} and 10a^{2} – 8b^{2} – 5ab

Arrange the like terms and then add,

=5a^{2} + 10a^{2} + 3ab -5ab + 2b^{2} -8b^{2}

=15a^{2} -2ab-6b^{2}

Hence, By adding the trinomials 5a^{2} + 3ab + 2b^{2} and 10a^{2} – 8b^{2} – 5ab we get 15a^{2} -2ab-6b^{2}.

(iii) Given trinomials are 18mn + 10np + 15mp and 10mn – 13np + 14mp

Arrange the like terms and then add,

=18mn+10mn+10np-13np+15mp+14mp

=28mn-3np+29mp

Hence, By adding 18mn + 10np + 15mp and 10mn – 13np + 14mp we get 28mn-3np+29mp.

**IV. Add the following expressions:
**(i) 6xyz + 2yz + 7zx, 4xz – 5yz + xyz and -2xyz – 12zy + 7xz

(ii) 2x

^{3}– y

^{3}+ 3x, 4y

^{3}– x

^{3}+ 6x and -y + 4y

^{3}– 2x + 3x

^{3}

(iii) 5p

^{2}– 3p

^{2}q + 7q

^{2}, q

^{2}– 3p

^{2}+ 16p

^{2}q and 8p

^{2}q + 9p

^{2}

(iv) 7x

^{2}– 6x + 3, -13x

^{2}– 4 + 12x and 25x

^{2}+ 20x – 15

(v) –3m

^{2}– 2mn + 5n

^{2}+ 5, 2m

^{2}– 3n

^{2}– 2 + 2mn and -5mn + 3m

^{2}– 3 + 2n

^{2}

(vi) 5x

^{2}+2x-5, 2x

^{2}-4x-7 and 12x

^{2}+9x+9

**Solution:**

(i) Given 6xyz + 2yz + 7zx, 4xz – 5yz + xyz and -2xyz – 12zy + 7xz

Arrange the like terms and then add,

=6xyz+xyz-2xyz+2yz-5yz-12zy+7zx+4xz+7xz

=7xyz – 2xyz + 2yz – 12 zy + 11 zx +7xz

=5xyz -10yz + 18zx

Hence, By adding 6xyz + 2yz + 7zx, 4xz – 5yz + xyz and -2xyz – 12zy + 7xz we get 5xyz -10yz + 18zx.

(ii) Given 2x^{3} – y^{3} + 3x, 4y^{3} – x^{3} + 6x and -y + 4y^{3} – 2x + 3x^{3}

Arrange the like terms and then add,

=2x^{3}– x^{3} +3x^{3} + 3x +6x-2x-y^{3}+4y^{3}+4y^{3
}=4x^{3}+7x+7y^{3
}Hence, By adding 2x^{3} – y^{3} + 3x, 4y^{3} – x^{3} + 6x and -y + 4y^{3} – 2x + 3x^{3} is 4x^{3}+7x+7y^{3}.

(iii) Given 5p^{2} – 3p^{2}q + 7q^{2}, q^{2} – 3p^{2} + 16p^{2}q and 8p^{2}q + 9p^{2}

Arrange the like terms and then add,

=5p^{2}-3p^{2}+9p^{2}-3p^{2}q +16p^{2}q +8p^{2}q +7q^{2}+q^{2}

=11p^{2} + 21p^{2}q +8q^{2
}Hence, By adding 5p^{2} – 3p^{2}q + 7q^{2}, q^{2} – 3p^{2} + 16p^{2}q and 8p^{2}q + 9p^{2} we get 11p^{2} + 21p^{2}q +8q^{2 }

(iv) Given 7x^{2} – 6x + 3, -13x^{2} – 4 + 12x and 25x^{2} + 20x – 15

Arrange the like terms and then add,

7x^{2}-13x^{2}+25x^{2}-6x+12x+20x+3-4-15

=32x^{2}-13x^{2} +32x-6x+3-19

=19x^{2}+26x-16

Hence, By adding 7x^{2} – 6x + 3, -13x^{2} – 4 + 12x and 25x^{2} + 20x – 15 we get 19x^{2}+26x-16.

(v) Given –3m^{2} – 2mn + 5n^{2} + 5, 2m^{2} – 3n^{2} – 2 + 2mn and -5mn + 3m^{2} – 3 + 2n^{2}

Arrange the like terms and then add,

=-3m^{2}+2m^{2}+3m^{2}-2mn+2mn-5mn+5n^{2}-3nn^{2}+2n^{2}+5-2-3

=2m^{2}-5mn+4n^{2}

Hence, By adding –3m^{2} – 2mn + 5n^{2} + 5, 2m^{2} – 3n^{2} – 2 + 2mn and -5mn + 3m^{2} – 3 + 2n^{2} we get 2m^{2}-5mn+4n^{2}.

(vi) Given, 5×2+2x-5, 2×2-4x-7 and 12×2+9x+9

Arrange the like terms and then add,

=5×2+2×2+12×2+2x-4x+9x-5-7+9

=19×2+11x-4x-12+9

=19×2+7x-3

Hence, By adding 5×2+2x-5, 2×2-4x-7 and 12×2+9x+9 we get 19×2+7x-3.

**V. Find the sum of the following expressions:
**(i) 6x

^{2}– 3xy + y

^{2}and – 2x

^{2}+ 4xy – 3y

^{2}

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

(iii) 4a

^{2}+ 2ab – 3b

^{2}, -a

^{2}+ 3ab + 4b

^{2}and 3a

^{2}– 12ab + 5b

^{2}

(iv) m

^{2}– m+ 1, -5m

^{2}+ 2m – 2 and 3m

^{2}– 3m + 1

(v) a

^{2}– 2ab + bc, 4ab + bc – 3a

^{2}and -4bc + 2a

^{2}+ ab

(vi) 4m

^{2}+ 7 – 3m, 4m – m

^{2}+ 8 and -10 + 5m – 2m

^{2}

**Solution:**

(i) Given, 6x^{2} – 3xy + y^{2} and – 2x^{2} + 4xy – 3y^{2}

Arrange the like terms and then add,

=6x^{2}-2x^{2}-3xy+4xy+y^{2}-3y2

=4x^{2}+xy-2y^{2}

Hence,By adding 6x^{2} – 3xy + y^{2} and – 2x^{2} + 4xy – 3y^{2} we get 4x^{2}+xy-2y^{2}.

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

Arrange the like terms and then add,

=2p + 3q + 5r+ (-7p + q – 4r) + 6p – q – 5r

=2p + 3q + 5r -7p +q -4r +6p -q -5r

=8p-7p+3q+q-q+5r-4r-5r

=p+3q-4r

Hence, the sum of 2p + 3q + 5r, -7p + q – 4r and 6p – q – 5r is p+3q-4r.

(iii) Given, 4a^{2} + 2ab – 3b^{2}, -a^{2} + 3ab + 4b^{2} and 3a^{2} – 12ab + 5b^{2}

Arrange the like terms and then add,

=4a^{2}-a^{2}+3a^{2}+2ab+3ab-12ab-3b^{2}+4b^{2}+5b^{2}

=7a^{2}-a^{2}+5ab-12ab-3b^{2}+9b^{2}

=6a^{2}– 7ab + 6b^{2
}Hence, the sum of 4a^{2} + 2ab – 3b^{2}, -a^{2} + 3ab + 4b^{2} and 3a^{2} – 12ab + 5b^{2} is 6a^{2}– 7ab + 6b^{2}.

(iv) Given, m^{2} – m+ 1, -5m^{2} + 2m – 2 and 3m^{2} – 3m + 1

Arrange the like terms and then add,

=m^{2}-5m^{2}+3m^{2}-m+2m-3m+1-2+1

=4m^{2}-5m^{2}+2m-4m+2-2

=-m^{2}-2m

Hence, the sum of m^{2} – m+ 1, -5m^{2} + 2m – 2 and 3m^{2} – 3m + 1 is -m^{2}-2m.

(v) Given, a^{2} – 2ab + bc, 4ab + bc – 3a^{2} and -4bc + 2a^{2} + ab

Arrange the like terms and then add,

=a^{2}-3a^{2}+2a^{2}-2ab+4ab+ab+bc+bc-4bc

=3a^{2}-3a^{2}-2ab+5ab+2bc-4bc

=3ab-2bc

Hence, the sum of a^{2} – 2ab + bc, 4ab + bc – 3a^{2} and -4bc + 2a^{2} + ab is 3ab-2bc.

(vi) Given, 4m^{2} + 7 – 3m, 4m – m^{2} + 8 and -10 + 5m – 2m^{2}

Arrange the like terms and then add,

=4m^{2}– m^{2}– 2m^{2}-3m+4m+5m+7+8-10

=4m^{2}-3m^{2}-3m+9m+15-10

=m^{2}+6m+5

Hence, the sum of 4m^{2} + 7 – 3m, 4m – m^{2} + 8 and -10 + 5m – 2m^{2} is m^{2}+6m+5.