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) 6mn

^{2}from 18mn

^{2}

(ii) 4m

^{2}n from 10m

^{2}n

**(iii) -2pq from -35pq**

**Solution:**

(i) Given monomials are 6mn^{2} ,18mn^{2
}subtract 6mn^{2} from 18mn^{2}

=18mn^{2}-6mn^{2}

=12mn^{2
}Hence, By subtracting 6mn^{2} from 18mn^{2} we get 12mn^{2}.

(ii) Given monomials are 4m^{2}n,10m^{2}n

Subtract 4m^{2}n from 10m^{2}n

=10m^{2}n – 4m^{2}n

=6m^{2}n

Hence, By subtracting 4m^{2}n from 10m^{2}n we get 6m^{2}n.

(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) 7ab

^{3}+ 5b from 19ab

^{3}+ 20b

(iii) 3a – 6a

^{2}b from 8a+ 15a

^{2}b

**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 7ab^{3} + 5b,19ab^{3} + 20b

Subtract 7ab^{3} + 5b from 19ab^{3} + 20b

=19ab^{3} + 20b-(7ab^{3} + 5b)

=19ab^{3} + 20b-7ab^{3}-5b

Arrange the like terms and then subtract,

=19ab^{3}-7ab^{3}+20b-5b

=12ab^{3}+15b

Hence, By subtracting 7ab^{3} + 5b from 19ab^{3} + 20b we get 12ab^{3}+15b.

(iii) Given binomials are 3a – 6a^{2}b, 8a + 15a^{2}b

Subtract 3a – 6a^{2}b from 8a + 15a^{2}b

=8a + 15a^{2}b-(3a-6a^{2}b)

=8a+15a^{2}b+6a^{2}b-3a

Arrange the like terms and then subtract,

=15a^{2}b+6a^{2}b+8a-3a

=21a^{2}b+5a

Hence, By subtracting 3a – 6a^{2}b from 8a + 15a^{2}b we get 21a^{2}b+5a .

**
III. Arrange and subtract the trinomials:
**(i) -6a – 14b + 18c from 4a – 3b – c

(ii) 9 + 4x + 10x

^{2}from 3 – 2x – 7x

^{2}

(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 + 10x^{2} , 3 – 2x – 7x^{2}

Subtract 9 + 4x + 10x^{2} from 3 – 2x – 7x^{2
}=3 – 2x – 7x^{2}-(9 + 4x + 10x^{2})

=3-2x-7x^{2}-9-4x-10x^{2}

Arrange the like terms and then subtract,

=-7x^{2}-10x^{2}-4x-2x-6

=-17x^{2}-6x-6

Hence, By subtracting 9 + 4x + 10x^{2} from 3 – 2x – 7x^{2} we get -17x^{2}-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 m^{2}n – n + 8, 3m^{2}n – 4n + 7

Subtract m^{2}n – n + 8 from 3m^{2}n – 4n + 7

=3m^{2}n – 4n + 7-(m^{2}n – n + 8)

Arrange the like terms and then subtract,

=3m^{2}n-m^{2}n-4n+n+7-8

=2m^{2}n-3n-1

Hence, By subtracting m^{2}n – n + 8 from 3m^{2}n – 4n + 7 we get 2m^{2}n-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) 2x

^{2}– y

^{2}+ 6x – 4 from 8x

^{2}– 4xy + 5y

^{2}+ 3x – 3

(ii) 5mn – 2m

^{2}– 3n

^{2}from 5m

^{2}+ n

^{2}+ 2mn

(iii) x

^{2}– 5xy – y

^{2}from 2×2 + 8y

^{2}+ 8xy

**Solution:**

(i) Given, Subtract 2x^{2} – y^{2} + 6x – 4 from 8x^{2} – 4xy + 5y^{2} + 3x – 3

=8x^{2} – 4xy + 5y^{2} + 3x – 3-(2x^{2} – y^{2} + 6x – 4)

=8x^{2} – 4xy + 5y^{2}+y^{2} + 3x – 3-2x^{2}+y^{2}-6x+4

Arrange the like terms and then subtract,

=8x^{2}-2x^{2} – 4xy + 5y^{2}+y^{2} + 3x -6x+4- 3

=6x^{2}-4xy+6y^{2}-3x+1

Hence, By subtracting 2x^{2} – y^{2} + 6x – 4 from 8x^{2} – 4xy + 5y^{2} + 3x – 3 we get 6x^{2}-4xy+6y^{2}-3x+1.

(ii) Given, Subtract 5mn – 2m^{2} – 3n^{2} from 5m^{2} + n^{2} + 2mn

=5m^{2} + n^{2} + 2mn-(5mn – 2m^{2} – 3n^{2})

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

Arrange the like terms and then subtract,

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

=7m^{2} -3mn-2n^{2}

Hence By subtracting 5mn – 2m^{2} – 3n^{2} from 5m^{2} + n^{2} + 2mn we get 7m^{2} -3mn-2n^{2} .

(iii) Given, Subtract x^{2}– 5xy – y^{2} from 2x^{2} + 8y^{2} + 8xy

=2x^{2} + 8y^{2} + 8xy-(x^{2}– 5xy – y^{2})

=2x^{2} + 8y^{2} + 8xy-x^{2}+5xy+y^{2}

Arrange the like terms and then subtract,

=2x^{2}-x^{2}+8y^{2}+y^{2}+8xy+5xy

=x^{2}+9y^{2}+13xy

Hence, By subtracting x^{2}– 5xy – y^{2} from 2x^{2} + 8y^{2} + 8xy we get x^{2}+9y^{2}+13xy.

**VI.** What must be subtracted from 2x^{2} + 3x – 2 to obtain x^{2} – 3x?

**Solution:**

Let p(x) be the polynomial that must be subtracted from 2x^{2} + 3x – 2 to obtain x^{2} – 3x.

2x^{2} + 3x – 2-p(x)=x^{2} – 3x

2x^{2} + 3x – 2-(x^{2} – 3x)=p(x)

2x^{2} + 3x – 2-x^{2}+3x=p(x)

x^{2}+6x-2=p(x)

Hence,x^{2}+6x-2 must be subtracted from 2x^{2} + 3x – 2 to obtain x^{2} – 3x.