Worksheet on Adding and Subtracting Like Terms will help you learn how to simplify expressions. While Adding and Subtracting Like Terms we need to collect different groups of like terms and then find the sum and difference in each group. Practice using the Addition and Subtraction of Like Terms Worksheet and learn how questions are framed on the topic.
Use the Adding and Subtracting Like Terms Practice Worksheet as a self-assessment to test your understanding of the topic and improve on the areas of need. Download the Simplifying and Combining Like Terms Worksheet PDF and learn how to add and subtract like terms in algebraic expressions.
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Adding and Subtracting Like Terms Worksheet PDF
I. Add the following terms
(i) 2a, -4a, -5a and 6a
(ii) 3x3, -6x3, 2x3 and -x3
(iii) 2abc, -8abc, -4abc and 6abc
(iv) 7x2y2, -2x2y2, 6x2y2 and -4x2y2
(v) -5a2b, 3ba2, -7ba2, 13a2b and -2a2b
(vi) 5xy, -3xy, 8xy, -2xy and 2xy
(vii) 10mn, -14mn, 2mn, – 8mn and 6mn
(viii) -4abz, 12abz, -5abz and 7abz
Solution:
(i) Given 2a, -4a, -5a and 6a
Add the given terms,
=2a+(-4a)+(-5a)+6a
=2a-4a-5a+6a
=2a-9a+6a
=8a-9a
=-a
(ii) Given 3x3, -6x3, 2x3 and -x3
Add the given terms,
=3x3+(-6x3)+2x3+(-x3)
=3x3-6x3+2x3-x3
=5x3-7x3
=-2x3
(iii) Given 2abc, -8abc, -4abc and 6abc
Add the given terms,
=2abc+(-8abc)+(-4abc)+6abc
=2abc-8abc-4abc+6abc
=2abc-12abc+6abc
=8abc-12abc
=-4abc
(iv) Given 7x2y2, -2x2y2, 6x2y2 and -4x2y2
By adding the given terms,
=7x2y2+(-2x2y2)+6x2y2 +(-4x2y2)
=7x2y2-2x2y2+6x2y2 -4x2y2
=7x2y2+6x2y2-6x2y2
=7x2y2
(v)Given -5a2b, 3ba2, -7ba2, 13a2b and -2a2b
By adding the given terms,
=-5a2b+3ba2+(-7ba2)+13a2b+(-2a2b)
=-5a2b+3ba2-7ba2+13a2b-2a2b
=-14a2b+16a2b
=2a2b
(vi)Given 5xy, -3xy, 8xy, -2xy and 2xy
By adding the given terms,
=5xy+(-3xy)+8xy+(-2xy)+2xy
=5xy-3xy+8xy-2xy+2xy
=2xy+6xy+2xy
=10xy
(vii) Given 10mn, -14mn, 2mn, – 8mn and 6mn
By adding the given terms,
=10mn+(-14mn)+2mn+(-8mn)+6mn
=10mn-14mn+2mn-8mn+6mn
=18mn-22mn
=-4mn
(viii) Given, -4abz, 12abz, -5abz and 7abz
By adding the given terms,
=-4abz+12abz-5abz+7abz
=-9abz+19abz
=10abz
II. Subtract the following terms
(i) 8y from 18y
(ii) 5x from -18x
(iii) 5x2 from 9x2
(iv) 18a2 from 10a2
(v) -14x2y2 from 2x2y2
(vi) 10xy from 19xy
(vii) 17a5b7 from 15a57
(viii) m4n2 from 6n2m4
(ix) -8abcd from 3abcd
Solution:
(i) Given
subtract 8y from 18y
18y-8y=10y
Hence, By subtracting 8y from 18y we get 10y.
(ii) Given
Subtract 5x from -18x
-18x-5x=-23x
Hence, By subtracting 5x from -18x we get -23x.
(iii) Given
Subtract 5x2 from 9x2
9x2-5x2=4x2
Hence, By subtracting 5x2from 9x2 we get 4x2.
(iv) Given
Subtract 18a2 from 10a2
10a2 -18a2=-8a2
Hence, By subtracting 18a2 from 10a2 we get -8a2.
(v) Given
Subtract-14x2y2 from 2x2y2
=2x2y2-(-14x2y2)
=2x2y2+142x2y2
=16x2y2
Hence, By subtracting -14x2y2 from 2x2y2 we get 16x2y2.
(vi)Given
Subtract 10xy from 19xy
=19xy-10xy
=9xy
Hence, By subtracting 10xy from 19xy we get 9xy.
(vii)Given
Subtract 17a5b7 from 15a5b7
=17a5b7 – 15a5b7
=2a5b7
Hence, By subtracting 17a5b7 from 15a5b7 we get 2a5b7.
(viii) Given
Subtract m4n2 from 6n2m4
=m4n2-6n2m4=-5m4n2
Hence, By subtracting m4n2 from 6n2m4 we get -5m4n2.
(ix) -8abcd from 3abcd
=3abcd – 8abcd
=-5abcd
Hence, By subtracting -8abcd from 3abcd we get -5abcd.
III. Find the sum of
(i) 2a, 15a, 6a and 22a
(ii) -2m, -4m, -m and 10m
(iii) 3xy, 5xy, -4xy, -2xy and 7xy
(iv) 8a, 3a, -5a, -a, -2a and a
(v) 3p, -2p, -8p, -13p and 19p
(vi) 4z, 3z, -2z, -z, 6z, 8z and z
Solution:
(i) Given 2a, 15a, 6a and 22a
=2a+15a+6a+22a
=44a
Therefore, the sum of 2a, 15a, 6a and 22a is 44a.
(ii) Given -2m, -4m, -m and 10m
=-2m+(-4m)+(-m)+10m
=-2m-4m-m+10m
=-7m+10m
=3m
Therefore, the sum of -2m, -4m, -m and 10m is 3m.
(iii) Given 3xy, 5xy, -4xy, -2xy and 7xy
=3xy+ 5xy+(-4xy)+ (-2xy) + 7xy
=8xy-4xy-2xy+7xy
=8xy-6xy+7xy
=2xy+7xy
=9xy
Therefore, the sum of 3xy, 5xy, -4xy, -2xy and 7xy is 9xy.
(iv) Given 8a, 3a, -5a, -a, -2a and a
=8a+3a+ (-5a)+ (-a)+(-2a)+ a
=11a-5a-a-2a+a
=12a-8a
=4a
Therefore, the sum of 8a, 3a, -5a, -a, -2a and a is 4a.
(v) Given 3p, -2p, -8p, -13p and 19p
=3p+ (-2p)+ (-8p)+(-13p)+ 19p
=3p-2p-8p-13p+19p
=22p-23p
=-p
Therefore, the sum of 3p, -2p, -8p, -13p and 19p is -p.
(vi) Given 4z, 3z, -2z, -z, 6z, 8z and z
=4z+3z-2z-z+6z+8z+z
=7z-3z+15z
=22z-3z
=19z
Therefore, the sum of 4z, 3z, -2z, -z, 6z, 8z, and z is 19z.
Iv. Simplify by combining like terms
(i) 5a2 – 11a + 4a2 + 2a
(ii) 4x3 – 8x2 + 12x2 – 15x3
(iii) -13x2y + 9xy2 – 5x2y + xy2
(iv) a3 + a2 + a – 3a + 5a2 – 9a3
(v) -8a3b2 + 10a2b3 – 8a3b2 – 8a2b3 + 5a3b2
(vi) 4x – 3y + 6z + 8x + 8y – 4z
(vii) x – 4y – 7z + 4z + 9x– 7y -3z + x – 5y
(viii) xy + 2yz – 3zx + 5xy + 6zx – 2yz + 8xy – 5yz + 3xz – 3xz
Solution:
(i) Given,
5a2 – 11a + 4a2 + 2a
By combining the like terms,
=5a2+4a2-11a+2a
=9a2-9a
Hence, By simplifying the like terms 5a2 – 11a + 4a2 + 2a=9a2-9a
(ii) Given,
=4x3 – 8x2 + 12x2 – 15x3
By combining the like terms,
=4x3 -15x3-8x2+12x2
=-11x3+4x2
Hence, By simplifying the like terms 4x3 – 8x2 + 12x2 – 15x3 =-11x3+4x2
(iii) Given,
-13x2y + 9xy2 – 5x2y + xy2
By combining the like terms,
=-13x2y-5x2y+9xy2+xy2
=-18x2y+10xy2
Hence, By simplifying the like terms -13x2y + 9xy2 – 5x2y + xy2=-18x2y+10xy2
(iv) Given,
a3 + a2 + a – 3a + 5a2 – 9a3
By combining the like terms,
=a3-9a3+a2+5a2+a-3a
=-8a3+6a2-2a
Hence, By simplifying the like terms a3 + a2 + a – 3a + 5a2 – 9a3= -8a3+6a2-2a.
(v) Given,
-8a3b2 + 10a2b3 – 8a3b2 – 8a2b3 + 5a3b2
By combining the like terms,
=-8a3b2-8a3b2+5a3b2+10a2b3-8a2b3
=-16a3b2+5a3b2+2a2b3
=-11a3b2+2a2b3
Hence, By simplifying the like terms -8a3b2 + 10a2b3 – 8a3b2 – 8a2b3 + 5a3b2=-11a3b2+2a2b3.
(vi) Given,
4x – 3y + 6z + 8x + 8y – 4z
By combining the like terms,
=4x+8x-3y+8y+6z-4z
=12x+5y+2z
Hence, By simplifying the like terms 4x – 3y + 6z + 8x + 8y – 4z=12x+5y+2z.
(vii) Given,
x – 4y – 7z + 4z + 9x– 7y -3z + x – 5y
By combining the like terms,
=x+9x+x-4y-7y-5y+4z-3z-7z
=11x-16y-6z
Hence, By simplifying the like terms x – 4y – 7z + 4z + 9x– 7y -3z + x – 5y=11x-16y-6z.
(viii) Given,
xy + 2yz – 3zx + 5xy + 6zx – 2yz + 8xy – 5yz + 3xz – 3xz
By combining the like terms,
=xy+5xy+8xy+2yz-2yz-5yz-3zx+6zx-3xz-3xz
=14xy-5yz-3xz
Hence, By simplifying the like terms xy + 2yz – 3zx + 5xy + 6zx – 2yz + 8xy – 5yz + 3xz – 3xz=14xy-5yz-3xz.