 Mathematics deals with four arithmetic operations in general and Subtraction is one among them. Subtraction of Algebraic Expressions is more of Subtraction of Numbers. The only difference is we need to identify and collect like and unlike terms. This Worksheet on Subtraction of Unlike Terms has different questions asked for simplifying algebraic expressions.

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• Worksheet on Addition of Unlike Terms
• Worksheet on Adding and Subtracting Like Terms

Simplifying Algebraic Expressions by Subtracting Unlike Terms Worksheet

I. Subtract the following:
(i) from 7ab take a
(ii) from 19a2bc take 7abc
(iii) from -4yz take 10xz
(iv) from a2 take b2
(v) from 25ab take 7b
(vi) from 35mn take 20np

Solution:

(i) Subtract a from 7ab
7ab-a
Hence, By subtracting a from 7ab we get 7ab-a.
(ii) subtract 7abc from 19a2bc
19a2bc-7abc
Hence, By subtracting 7abc from 19a2bc we get 19a2bc-7abc.
(iii) subtract 10xz from -4yz
-4yz-10xz
Hence, By subtracting 10xz from -4yz we get -4yz-10xz.
(iv) subtract b2 from a2.
a2-b2
Hence, By subtracting b2 from a2 we get a2-b2.
(v) subtract 7b from 25 ab
=25ab-7b
Hence, By subtracting 7b from 25ab we get 25ab-7b.
(vi) Subtract 20np from 35mn
=35mn-20np
Hence, By subtracting 20np from 35mn we get 35mn-20np.

II. Find the difference of:
(i) 4a from 18b
(ii) 10m2 from 6mn
(iii) 18x2 from 12x2y
(iv) 2b from 6ab
(v) 3y3 from 12y2
(vi) ab2 from a2b

Solution:

(i) Subtract 4a from 18b
18b – 4a
Therefore, the difference of 4a from 18b is 18b – 4a.
(ii) Subtract 10m2 from 6mn
=6mn-10m2
Therefore, the difference of 10m2 from 6mn is 6mn-10m2.
(iii) Subtract 18x2 from 12x2y
=12x2y- 18x2
Therefore, the difference of 18x2 from 12x2y is 12x2y- 18x2.
(iv) Subtract 2b from 6ab
=6ab-2b
Therefore, the difference of 2b from 6ab is 6ab-2b.
(v) Subtract 3y3 from 12y2
=12y2-3y3
Therefore, the difference of 3y3 from 12y2 is 12y2-3y3.
(vi) Subtract ab2 from a2b
=a2b-ab2
Therefore, the difference of ab2 from a2b is a2b-ab2.

III. Subtract the first term from the second term:
(i) 7x, 18y
(ii) 6mn, n2
(iii) 2z, 7y
(iv) pq, 18p
(v) 3pq, 2mn
(vi) 24mnp, 20mn

Solution:

(i) Given, 7x, 18y
Subtract the first term from the second term,
=18y-7x
Hence, By subtracting 7x from 18y we get 18y-7x.
(ii) Given, 6mn, n2
Subtract the first term from the second term,
=n2-6mn
Hence, By subtracting 6mn from n2 we get n2-6mn.
(iii) Given, 2z, 7y
Subtract the first term from the second term,
=7y-2z
Hence, By subtracting 2z from 7y we get 7y-2z.
(iv) Given, pq, 18P
Subtract the first term from the second term,
=18P-pq
Hence, By subtracting pq from 18P we get 18P-pq.
(v) Given, 3pq, 2mn
Subtract the first term from the second term,
=2mn-3pq
Hence, By subtracting 3pq from 2mn we get 2mn-3pq.
(vi) given, 24mnp, 20mn
Subtract the first term from the second term,
=20mn-24mnp
Hence, By subtracting 24mnp from 20mn we get 20mn-24mnp.

IV. Evaluate the following:
(i) 2x + 5y – 3y
(ii) 2m + 5n + m – n
(iii) 7ab – 3b – 2ab
(iv) x – 3y – 2x + 15y
(v) -2ab – 5ab – 6ay
(vi) 4x2 – 2y2 – x2
(vii) 5mn+km-mn+3km

Solution:

(i) Given, 2x + 5y – 3y
=2x+2y
Therefore, By evaluating 2x + 5y – 3y we get 2x+2y.
(ii) Given, 2m + 5n + m – n
=2m+m+5n-n
=3m+4n
Therefore, By evaluating 2m + 5n + m – n we get 3m+4n.
(iii) Given, 7ab – 3b – 2ab
=7ab-2ab-3b
=5ab-3b
Therefore, By evaluating 7ab – 3b – 2ab we get 5ab-3b.
(iv) Given, x – 3y – 2x + 15y
=x-2x-3y+15y
=-x+12y
Therefore, By evaluating x – 3y – 2x + 15y we get -x+12y.
(v) Given, -2ab – 5ab – 6ay
=-7ab-6ay
Therefore, By evaluating -2ab – 5ab – 6ay we get -7ab-6ay .
(vi) Given, 4x2 – 2y2 – x2
=4x2 -x2 -2y2
=3x2 -2y2
Therefore, By evaluating 4x2 – 2y2 – x2 we get 3x2 -2y2.
(vii) Given, 5mn+km-mn+3km
=5mn-mn+km+3km
=4mn+4km
Therefore, By evaluating 5mn+km-mn+3km we get 4mn+4km.

V. Find the difference between
(i) 15xy,2y2
(ii) -28mn,2m3n

Solution:

(i) Given 15xy,2y2
=15xy-2y2
Therefore, the difference between 15xy,2y2 is 15xy-2y2.
(ii) Given -28mn,2m3n
=-28nm-2m3n
Therefore, the difference between -28mn,2m3n is -28nm-2m3n.

VI.  How much is 4x + 3y greater than 2y?

Solution:

=4x+3y-2y
=4x+y
Therefore, 4x+3y is greater than 2y by 4x+y.