Worksheets on Addition of Polynomials

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) 5a2b2 and 9a2b2
(iii) 5a5, and -3a5

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 5a2b2 and 9a2b2
=5a2b2 + 9a2b2
= 14 a2b2
Hence, By adding 5a2b2 and 9a2b2 we get 14 a2b2 .
(iii) Given monomials are 5a5, and -3a5
=5a5+(-3a5)
=5a5-3a5
=2a 5
Hence, By adding 5a5 and -3a5 we get 2a 5.


II. Arrange and add the binomials:
(i) 6m + 8n and 4m + 2n
(ii) 17a -5b and -3a+ 15b
(iii) 4a2b + 2b and -10a2b + 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 4a2b + 2b and -10a2b + 5b
Arrange the like terms and then add,
=4a2b -10a2b + 2b + 5b
=-6a2b+7b


III. Arrange and add the trinomials:
(i) 3x + 2y – z and 14x – 7y + 2z
(ii) 5a2 + 3ab + 2b2 and 10a2 – 8b2 – 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 5a2 + 3ab + 2b2 and 10a2 – 8b2 – 5ab
Arrange the like terms and then add,
=5a2 + 10a2 + 3ab -5ab + 2b2 -8b2
=15a2 -2ab-6b2
Hence, By adding the trinomials 5a2 + 3ab + 2b2 and 10a2 – 8b2 – 5ab we get 15a2 -2ab-6b2.
(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) 2x3 – y3 + 3x, 4y3 – x3 + 6x and -y + 4y3 – 2x + 3x3
(iii) 5p2 – 3p2q + 7q2, q2– 3p2 + 16p2q and 8p2q + 9p2
(iv) 7x2 – 6x + 3, -13x2 – 4 + 12x and 25x2 + 20x – 15
(v) –3m2 – 2mn + 5n2 + 5, 2m2 – 3n2 – 2 + 2mn and -5mn + 3m2 – 3 + 2n2
(vi) 5x2+2x-5, 2x2-4x-7 and 12x2+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 2x3 – y3 + 3x, 4y3 – x3 + 6x and -y + 4y3 – 2x + 3x3
Arrange the like terms and then add,
=2x3– x3 +3x3 + 3x +6x-2x-y3+4y3+4y3
=4x3+7x+7y3
Hence, By adding 2x3 – y3 + 3x, 4y3 – x3 + 6x and -y + 4y3 – 2x + 3x3 is 4x3+7x+7y3.
(iii) Given 5p2 – 3p2q + 7q2, q2 – 3p2 + 16p2q and 8p2q + 9p2
Arrange the like terms and then add,
=5p2-3p2+9p2-3p2q +16p2q +8p2q +7q2+q2
=11p2 + 21p2q +8q2
Hence, By adding 5p2 – 3p2q + 7q2, q2 – 3p2 + 16p2q and 8p2q + 9p2 we get 11p2 + 21p2q +8q2
(iv) Given 7x2 – 6x + 3, -13x2 – 4 + 12x and 25x2 + 20x – 15
Arrange the like terms and then add,
7x2-13x2+25x2-6x+12x+20x+3-4-15
=32x2-13x2 +32x-6x+3-19
=19x2+26x-16
Hence, By adding 7x2 – 6x + 3, -13x2 – 4 + 12x and 25x2 + 20x – 15 we get 19x2+26x-16.

(v) Given –3m2 – 2mn + 5n2 + 5, 2m2 – 3n2 – 2 + 2mn and -5mn + 3m2 – 3 + 2n2
Arrange the like terms and then add,
=-3m2+2m2+3m2-2mn+2mn-5mn+5n2-3nn2+2n2+5-2-3
=2m2-5mn+4n2
Hence, By adding –3m2 – 2mn + 5n2 + 5, 2m2 – 3n2 – 2 + 2mn and -5mn + 3m2 – 3 + 2n2 we get 2m2-5mn+4n2.
(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) 6x2 – 3xy + y2 and – 2x2 + 4xy – 3y2
(ii) 2p + 3q + 5r, -7p + q – 4r and 6p – q – 5r
(iii) 4a2 + 2ab – 3b2, -a2 + 3ab + 4b2 and 3a2 – 12ab + 5b2
(iv) m2 – m+ 1, -5m2 + 2m – 2 and 3m2 – 3m + 1
(v) a2 – 2ab + bc, 4ab + bc – 3a2 and -4bc + 2a2 + ab
(vi) 4m2 + 7 – 3m, 4m – m2 + 8 and -10 + 5m – 2m2

Solution:

(i) Given, 6x2 – 3xy + y2 and – 2x2 + 4xy – 3y2
Arrange the like terms and then add,
=6x2-2x2-3xy+4xy+y2-3y2
=4x2+xy-2y2
Hence,By adding 6x2 – 3xy + y2 and – 2x2 + 4xy – 3y2 we get 4x2+xy-2y2.

(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, 4a2 + 2ab – 3b2, -a2 + 3ab + 4b2 and 3a2 – 12ab + 5b2
Arrange the like terms and then add,
=4a2-a2+3a2+2ab+3ab-12ab-3b2+4b2+5b2
=7a2-a2+5ab-12ab-3b2+9b2
=6a2– 7ab + 6b2
Hence, the sum of 4a2 + 2ab – 3b2, -a2 + 3ab + 4b2 and 3a2 – 12ab + 5b2 is 6a2– 7ab + 6b2.
(iv) Given, m2 – m+ 1, -5m2 + 2m – 2 and 3m2 – 3m + 1
Arrange the like terms and then add,
=m2-5m2+3m2-m+2m-3m+1-2+1
=4m2-5m2+2m-4m+2-2
=-m2-2m
Hence, the sum of m2 – m+ 1, -5m2 + 2m – 2 and 3m2 – 3m + 1 is -m2-2m.
(v) Given, a2 – 2ab + bc, 4ab + bc – 3a2 and -4bc + 2a2 + ab
Arrange the like terms and then add,
=a2-3a2+2a2-2ab+4ab+ab+bc+bc-4bc
=3a2-3a2-2ab+5ab+2bc-4bc
=3ab-2bc
Hence, the sum of a2 – 2ab + bc, 4ab + bc – 3a2 and -4bc + 2a2 + ab is 3ab-2bc.
(vi) Given, 4m2 + 7 – 3m, 4m – m2 + 8 and -10 + 5m – 2m2
Arrange the like terms and then add,
=4m2– m2– 2m2-3m+4m+5m+7+8-10
=4m2-3m2-3m+9m+15-10
=m2+6m+5
Hence, the sum of 4m2 + 7 – 3m, 4m – m2 + 8 and -10 + 5m – 2m2 is m2+6m+5.


 

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