In the Worksheet on Subtraction of Like Terms, you will learn how to subtract like terms in a given algebraic expression. Know different questions asked on the topic from Subtracting Like Terms Worksheet available here and master the concept. We have explained the different methods of Subtraction of Like Terms in an Algebraic Expression such as the Horizontal Method, Vertical Method, etc.
Practice the problems in the 6th Grade Math Subtraction of Like Terms Worksheet and if you are stuck at any point check out our step-by-step explanations. Download the Subtraction of Like Terms Worksheet for free and resolve your doubts if any and score better grades in exams.
Do Check:
- Worksheet on Adding and Subtracting Like Terms
- Worksheet on Subtraction of Unlike Terms
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Subtracting Like Terms Worksheet with Answers
I. Fill in the blanks:
(i) 9 – 5 = ____ and 9ab – 5ab = ____
(ii) 18 – 14 = ____ and 18xy – 14xy = ____
(iii) 6 – 15 = ____ and 6pq – 15pq = ____
(iv) 26 – 6 = ____ and 26abc – 6abc = ____
(v) 12 – 2 = ____ and 12xyz – 2xyz = ____
Solution:
(i) 4,4ab
(ii) 4,4xy
(iii) -9, -9pq
(iv) 20, 20abc
(v) 10, 10xyz
II. Subtract the first term from the second term:
(i) 8m, 10m
(ii) 4xy, 6yx
(iii) 5mn, 7mn
(iv) 15ab, 30ab
(v) 17x2y, 9x2y
(vi) 23pq, 18pq
Solution:
(i) Given 8m, 10m
Subtract the first term from the second term,
10m-8m=2m
Hence, 10m-8m is 2m.
(ii) Given 4xy, 6yx
Subtract the first term from the second term,
6yx-4xy=2xy
Hence, 6yx-4xy is 2xy.
(iii) Given 5mn, 7mn
Subtract the first term from the second term,
7mn-5mn=2mn
Hence, 7mn-5mn is 2mn.
(iv) Given 15ab, 30ab
Subtract the first term from the second term,
30ab-15ab=15ab
Hence, 30ab-15ab=15ab.
(v) Given 17x2y, 9x2y
By subtracting the first term from the second term we get,
9x2y-17x2y=-8x2y
Hence, 9x2y-17x2y=-8x2y
(vi) Given 23pq,18pq
By subtracting the first term from the second term we get,
18pq-23pq=-5pq
Hence,18pq-23pq=-5pq.
III. Subtract arranging the like terms:
(i) 4a – 7b from 10a – 14b + 4
(ii) –m3 + 3m2n + 2p3 from 9m3 – 5m2n – 4p3
(iii) 4a – 3b – 2c from a – 2b – 7c
(iv) From 4x3 – y3 + 2z3subtract 8x3 + y3 – z3
(v) From 7m2 – mn + 4n3 subtract 4m2 – 2nm – 3n3
(vi) From 6a4 + ab + 4b3 subtract 2a4 – 3ab – 2b3
Solution:
(i) 4a – 7b from 10a – 14b + 4
Here the like terms are 4a,-7b,10a,-14b
=10a – 14b + 4-(4a – 7b)
=10a-4a-14b+7b+4
=6a-7b+4
Hence, By subtracting 4a – 7b from 10a – 14b + 4 we get 6a-7b+4.
(ii) –m3 + 3m2n + 2p3 from 9m3 – 5m2n – 4p3
=9m3 – 5m2n – 4p3- ( –m3 + 3m2n + 2p3)
By arranging the like terms together, we get
=9m3+m3 –5m2n – 3m2n-4p3-2p3
=10m3-8m2n-6p3
Hence, By subtracting –m3 + 3m2n + 2p3 from 9m3 – 5m2n – 4p3 we get 10m3-8m2n-6p3 .
(iii) 8a – 4b – 2c from a – 2b – 7c
=a – 2b – 7c-(8a – 4b – 2c)
By arranging the like terms together, we get
=a-8a-2b+4b-7c+2c
=-7a+2b-5c
Hence, By subtracting 8a – 4b – 2c from a – 2b – 7c we get -7a+2b-5c.
(iv) From 4x3 – y3 + 2z3subtract 8x3 + y3 – z3
=4x3 – y3 + 2z3-(8x3 + y3 – z3)
By arranging the like terms together, we get
=4x3 -8x3 – y3-y3 + 2z3+z3
=-4x3-2y3 +3z3
Hence, By subtracting 4x3 – y3 + 2z3-8x3 + y3 – z3=-4x3-2y3 +3z3
(v) From 7m2 – mn + 4n3 subtract 4m2 – 2nm – 3n3
=7m2 – mn + 4n3-(4m2 – 2nm – 3n3)
By arranging the like terms together, we get
=7m2-4m2-mn+2mn+4n3+3n3
=3m2+mn+7n3
Hence,By subtracting 7m2 – mn + 4n3-4m2 – 2nm – 3n3 we get 3m2+mn+7n3.
(vi) From 6a4 + ab + 4b3 subtract 2a4 – 3ab – 2b3
=6a4 + ab + 4b3-(2a4 – 3ab – 2b3)
By arranging the like terms together, we get
=6a4-2a4+ab+3ab+4b3+2b3
=4a4+4ab+6b3
Hence, By subtracting 6a4 + ab + 4b3 – 2a4 – 3ab – 2b3=4a4+4ab+6b3
IV. The sum of two expressions is x – 2y + 4z if one of the terms is 4x – 8y – z, find the other.
Solution:
Given,
The sum of two expressions is= x-2y+4z
one of the terms=4x-8y-z
Let the other termbe x.
x=4x-8y-z-(x-2y+4z)
x=4x-8y-z-x+2y-4z
x=3x-6y-5z
Hence, other expression is 3x-6y-5z.
V. What should be subtracted from -8p + 4q – 2r to obtain 12p – 7q + 6r.
Solution:
Let the term subtracted be x.
-8p+4q-2r-x=12p-7q+6r
x=12p-7q+6r-(-8p+4q-2r)
x=12p-7q+6r+8p-4q+2r
x=20p-11q+8r
VI. How much is a3 + b3 + c3 less than -2a3 + 5b3 – 9c3?
Solution:
=-2a3 + 5b3 – 9c3– (a3 + b3 + c3)
=-2a3+5b3-9c3– a3 – b3 – c3
=-3a3+4b3-10c3
Hence, a3 + b3 + c3 less than -2a3 + 5b3 – 9c3=-3a3 +4b3-10c3