Printable Worksheet on Subtraction of Polynomials provided will help you learn subtraction of polynomial expression with single as well as multi variables. This Subtraction of Polynomials Worksheet has questions on subtracting monomials, binomials, polynomials with dual levels involving coefficients.

Subtracting Polynomials Worksheet with Answers gives students access to numerous questions that are well structured. The Free Math Worksheet on Subtracting Polynomials available here is flexible enough so that students can learn at their own pace and study as per their learning curve.

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## Subtraction of Polynomials Worksheet with Answers

I. Arrange and subtract the monomials:
(i) 6mn2 from 18mn2
(ii) 4m2n from 10m2n
(iii) -2pq from -35pq

Solution:

(i) Given monomials are 6mn2 ,18mn2
subtract 6mn2 from 18mn2
=18mn2-6mn2
=12mn2
Hence, By subtracting 6mn2 from 18mn2 we get 12mn2.

(ii) Given monomials are 4m2n,10m2n
Subtract 4m2n from 10m2n
=10m2n – 4m2n
=6m2n
Hence, By subtracting 4m2n from 10m2n we get 6m2n.
(iii) Given monomials are -2pq, -35pq
Subtract -2pq from -35pq
=-35pq-(-2pq)
=-35pq+2pq
=-33pq
Hence, By subtracting -2pq from -35pq we get -33pq.

II. Arrange and subtract the binomials:
(i) 10m – 8m from 20m – 10n
(ii) 7ab3 + 5b from 19ab3 + 20b
(iii) 3a – 6a2b from 8a+ 15a2b

Solution:

(i) Given binomials are 10m – 8n, 20m – 10n
Subtract 10m – 8n from 20m – 10n
=20m – 10n – (10m-8n)
=20m-10n-10m+8n
Arrange the like terms and then subtract,
=20m-10m-10n+8n
=10m-2n
Hence, By subtracting 10m – 8n from 20m – 10n we get 10m-2n.
(ii) Given binomials are 7ab3 + 5b,19ab3 + 20b
Subtract 7ab3 + 5b from 19ab3 + 20b
=19ab3 + 20b-(7ab3 + 5b)
=19ab3 + 20b-7ab3-5b
Arrange the like terms and then subtract,
=19ab3-7ab3+20b-5b
=12ab3+15b
Hence, By subtracting 7ab3 + 5b from 19ab3 + 20b we get 12ab3+15b.

(iii) Given binomials are 3a – 6a2b, 8a + 15a2b
Subtract 3a – 6a2b from 8a + 15a2b
=8a + 15a2b-(3a-6a2b)
=8a+15a2b+6a2b-3a
Arrange the like terms and then subtract,
=15a2b+6a2b+8a-3a
=21a2b+5a
Hence, By subtracting 3a – 6a2b from 8a + 15a2b we get 21a2b+5a .

III. Arrange and subtract the trinomials:
(i) -6a – 14b + 18c from 4a – 3b – c
(ii) 9 + 4x + 10x2 from 3 – 2x – 7x2
(iii) 6x + 3y – 4z from 7x – 3y + 5z

Solution:

(i) Given trinomials are -6a – 14b + 18c, 4a – 3b – c
Subtract -6a – 14b + 18c from 4a – 3b – c
=4a – 3b – c-(-6a-14b+18c)
=4a-3b-c+6a+14b-18c
Arrange the like terms and then subtract,
=4a+6a-3b+14b-c-18c
=10a+11b-19c
Hence, By subtracting -6a – 14b + 18c from 4a – 3b – c we get 10a+11b-19c.
(ii) Given trinomials are 9 + 4x + 10x2 , 3 – 2x – 7x2
Subtract 9 + 4x + 10x2 from 3 – 2x – 7x2
=3 – 2x – 7x2-(9 + 4x + 10x2)
=3-2x-7x2-9-4x-10x2
Arrange the like terms and then subtract,
=-7x2-10x2-4x-2x-6
=-17x2-6x-6
Hence, By subtracting 9 + 4x + 10x2 from 3 – 2x – 7x2 we get -17x2-6x-6.

(iii) Given trinomials are 6x + 3y – 4z, 7x – 3y + 5z
Subtract 6x + 3y – 4z from 7x – 3y + 5z
=7x – 3y + 5z-(6x + 3y – 4z)
=7x – 3y + 5z-6x-3y+4z
=x-6y+9z
Hence, By subtracting 6x + 3y – 4z from 7x – 3y + 5z we get x-6y+9z.

IV. Find the difference of:
(i) x – 2y – 5z from 7x – 4y – 8z
(ii) x – 3xy + 2y + 7 from 11x – 7xy + 2y – 3
(iii) 4pq + 6qr – 8rp from 6pq – 3qr – 3rp + 11pqr
(iv) m2n – n + 8 from 3m2n – 4n + 7
(v) 2ab + cd – ac – 2bd from ab – 2cd + 2ac + bd
(vi) 5 – p – 4q + 4r from 5p – 7q + 2r

Solution:

(i) Given x – 2y – 5z from 7x – 4y – 8z
Subtract x – 2y – 5z from 7x – 4y – 8z
=7x – 4y – 8z-(x – 2y – 5z)
Arrange the like terms and then subtract,
=7x-x-4y+2y-8z+5z
=6x-2y-3z
Hence, By subtracting x – 2y – 5z from 7x – 4y – 8z we get 6x-2y-3z.
(ii) Given x – 3xy + 2y + 7, 11x – 7xy + 2y – 3
Subtract x – 3xy + 2y + 7 from 11x – 7xy + 2y – 3
=11x – 7xy + 2y – 3-(x – 3xy + 2y + 7)
=11x – 7xy + 2y – 3-x+3xy-2y-7
Arrange the like terms and then subtract,
=11x-x-7xy+3xy+2y-2y-3-7
=10x-4xy-10
Hence, By subtracting x – 3xy + 2y + 7 from 11x – 7xy + 2y – 3 we get 10x-4xy-10.
(iii) Given 4pq + 6qr – 8rp, 6pq – 3qr – 3rp + 11pqr
Subtract 4pq + 6qr – 8rp from 6pq – 3qr – 3rp + 11pqr
=6pq – 3qr – 3rp + 11pqr-(4pq + 6qr – 8rp)
=6pq – 3qr – 3rp + 11pqr-4pq-6qr+8rp
Arrange the like terms and then subtract,
=6pq-4pq-3qr-6qr-3rp+8rp
=2pq-9qr+5rp
Hence, By subtracting 4pq + 6qr – 8rp from 6pq – 3qr – 3rp + 11pqr we get 2pq-9qr+5rp.
(iv) Given m2n – n + 8, 3m2n – 4n + 7
Subtract m2n – n + 8 from 3m2n – 4n + 7
=3m2n – 4n + 7-(m2n – n + 8)
Arrange the like terms and then subtract,
=3m2n-m2n-4n+n+7-8
=2m2n-3n-1
Hence, By subtracting m2n – n + 8 from 3m2n – 4n + 7 we get 2m2n-3n-1.
(v) Given 2ab + cd – ac – 2bd from ab – 2cd + 2ac + bd
Subtract 2ab + cd – ac – 2bd from ab – 2cd + 2ac + bd
=ab – 2cd + 2ac + bd-(2ab+cd-ac-2bd)
=ab – 2cd + 2ac + bd-2ab-cd+ac+2bd
Arrange the like terms and then subtract,
=ab-2ab-2cd-cd+2ac+ac+bd+2bd
=-ab-3cd+3ac+3bd
=-ab-3cd+3ac+3bd
Hence, By subtracting 2ab + cd – ac – 2bd from ab – 2cd + 2ac + bd we get -ab-3cd+3ac+3bd.
(vi) Given 5 – p – 4q + 4r, 5p – 7q + 2r
Subtract 5 – p – 4q + 4r from 5p – 7q + 2r
=5p – 7q + 2r -(5 – p – 4q + 4r)
=5p – 7q + 2r -5 +p +4q -4r
Arrange the like terms and then subtract,
=5p+p-7q+4q+2r-4r-5
=6p-3q-2r-5
Hence, By subtracting5 – p – 4q + 4r from 5p – 7q + 2r we get 6p-3q-2r-5.

V. Subtract the following expressions:
(i) 2x2 – y2 + 6x – 4 from 8x2 – 4xy + 5y2 + 3x – 3
(ii) 5mn – 2m2 – 3n2 from 5m2 + n2 + 2mn
(iii) x2– 5xy – y2 from 2×2 + 8y2 + 8xy

Solution:

(i) Given, Subtract 2x2 – y2 + 6x – 4 from 8x2 – 4xy + 5y2 + 3x – 3
=8x2 – 4xy + 5y2 + 3x – 3-(2x2 – y2 + 6x – 4)
=8x2 – 4xy + 5y2+y2 + 3x – 3-2x2+y2-6x+4
Arrange the like terms and then subtract,
=8x2-2x2 – 4xy + 5y2+y2 + 3x -6x+4- 3
=6x2-4xy+6y2-3x+1
Hence, By subtracting 2x2 – y2 + 6x – 4 from 8x2 – 4xy + 5y2 + 3x – 3 we get 6x2-4xy+6y2-3x+1.
(ii) Given, Subtract 5mn – 2m2 – 3n2 from 5m2 + n2 + 2mn
=5m2 + n2 + 2mn-(5mn – 2m2 – 3n2)
=5m2 + n2 + 2mn-5mn+2m2-3n2
Arrange the like terms and then subtract,
=5m2 +2m2 +2mn-5mn+n2 -3n2
=7m2 -3mn-2n2
Hence By subtracting 5mn – 2m2 – 3n2 from 5m2 + n2 + 2mn we get 7m2 -3mn-2n2 .
(iii) Given, Subtract x2– 5xy – y2 from 2x2 + 8y2 + 8xy
=2x2 + 8y2 + 8xy-(x2– 5xy – y2)
=2x2 + 8y2 + 8xy-x2+5xy+y2
Arrange the like terms and then subtract,
=2x2-x2+8y2+y2+8xy+5xy
=x2+9y2+13xy
Hence, By subtracting x2– 5xy – y2 from 2x2 + 8y2 + 8xy we get x2+9y2+13xy.

VI. What must be subtracted from 2x2 + 3x – 2 to obtain x2 – 3x?

Solution:

Let p(x) be the polynomial that must be subtracted from 2x2 + 3x – 2  to obtain x2 – 3x.
2x2 + 3x – 2-p(x)=x2 – 3x
2x2 + 3x – 2-(x2 – 3x)=p(x)
2x2 + 3x – 2-x2+3x=p(x)
x2+6x-2=p(x)
Hence,x2+6x-2 must be subtracted from 2x2 + 3x – 2  to obtain x2 – 3x.