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) 3x

^{3}, -6x

^{3}, 2x

^{3}and -x

^{3}

(iii) 2abc, -8abc, -4abc and 6abc

(iv) 7x

^{2}y

^{2}, -2x

^{2}y

^{2}, 6x

^{2}y

^{2}and -4x

^{2}y

^{2}

(v) -5a

^{2}b, 3ba

^{2}, -7ba

^{2}, 13a

^{2}b and -2a

^{2}b

(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 3x^{3}, -6x^{3}, 2x^{3} and -x^{3}

Add the given terms,

=3x^{3}+(-6x^{3})+2x^{3}+(-x^{3})

=3x^{3}-6x^{3}+2x^{3}-x^{3}

=5x^{3}-7x^{3}

=-2x^{3}

(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 7x^{2}y^{2}, -2x^{2}y^{2}, 6x^{2}y^{2} and -4x^{2}y^{2}

By adding the given terms,

=7x^{2}y^{2}+(-2x^{2}y^{2})+6x^{2}y^{2} +(-4x^{2}y^{2})

=7x^{2}y^{2}-2x^{2}y^{2}+6x^{2}y^{2} -4x^{2}y^{2}

=7x^{2}y^{2}+6x^{2}y^{2}-6x^{2}y^{2}

=7x^{2}y^{2}

(v)Given -5a^{2}b, 3ba^{2}, -7ba^{2}, 13a^{2}b and -2a^{2}b

By adding the given terms,

=-5a^{2}b+3ba^{2}+(-7ba^{2})+13a^{2}b+(-2a^{2}b)

=-5a^{2}b+3ba^{2}-7ba^{2}+13a^{2}b-2a^{2}b

=-14a^{2}b+16a^{2}b

=2a^{2}b

(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) 5x

^{2}from 9x

^{2}

(iv) 18a

^{2}from 10a

^{2}

(v) -14x

^{2}y

^{2}from 2x

^{2}y

^{2}

(vi) 10xy from 19xy

(vii) 17a

^{5}b

^{7}from 15a

^{5}

^{7}

(viii) m

^{4}n

^{2}from 6n

^{2}m

^{4}

(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 5x^{2} from 9x^{2}

9x^{2}-5x^{2}=4x^{2}

Hence, By subtracting 5x^{2}from 9x^{2} we get 4x^{2}.

(iv) Given

Subtract 18a^{2} from 10a^{2}

10a^{2} -18a^{2}=-8a^{2}

Hence, By subtracting 18a^{2} from 10a^{2} we get -8a^{2}.

(v) Given

Subtract-14x^{2}y^{2} from 2x^{2}y^{2}

=2x^{2}y^{2}-(-14x^{2}y^{2})

=2x^{2}y^{2}+142x^{2}y^{2}

=16x^{2}y^{2}

Hence, By subtracting -14x^{2}y^{2} from 2x^{2}y^{2} we get 16x^{2}y^{2}.

(vi)Given

Subtract 10xy from 19xy

=19xy-10xy

=9xy

Hence, By subtracting 10xy from 19xy we get 9xy.

(vii)Given

Subtract 17a^{5}b^{7} from 15a^{5}b^{7}

=17a^{5}b^{7} – 15a^{5}b^{7}

=2a^{5}b^{7}

Hence, By subtracting 17a^{5}b^{7} from 15a^{5}b^{7} we get 2a^{5}b^{7}.

(viii) Given

Subtract m^{4}n^{2} from 6n^{2}m^{4}

=m^{4}n^{2}-6n^{2}m^{4}=-5m^{4}n^{2}

Hence, By subtracting m^{4}n^{2} from 6n^{2}m^{4} we get -5m^{4}n^{2}.

(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) 5a^{2} – 11a + 4a^{2} + 2a

(ii) 4x^{3} – 8x^{2} + 12x^{2} – 15x^{3}

(iii) -13x^{2}y + 9xy^{2} – 5x^{2}y + xy^{2}

(iv) a^{3} + a^{2} + a – 3a + 5a^{2} – 9a^{3}

(v) -8a^{3}b^{2} + 10a^{2}b^{3} – 8a^{3}b^{2} – 8a^{2}b^{3} + 5a^{3}b^{2}

(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,

5a^{2} – 11a + 4a^{2} + 2a

By combining the like terms,

=5a^{2}+4a^{2}-11a+2a

=9a^{2}-9a

Hence, By simplifying the like terms 5a^{2} – 11a + 4a^{2} + 2a=9a^{2}-9a

(ii) Given,

=4x^{3} – 8x^{2} + 12x^{2} – 15x^{3}

By combining the like terms,

=4x^{3} -15x^{3}-8x^{2}+12x^{2}

=-11x^{3}+4x^{2}

Hence, By simplifying the like terms 4x^{3} – 8x^{2} + 12x^{2} – 15x^{3} =-11x^{3}+4x^{2}

(iii) Given,

-13x^{2}y + 9xy^{2} – 5x^{2}y + xy^{2}

By combining the like terms,

=-13x^{2}y-5x^{2}y+9xy^{2}+xy^{2}

=-18x^{2}y+10xy^{2}

Hence, By simplifying the like terms -13x^{2}y + 9xy^{2} – 5x^{2}y + xy^{2}=-18x^{2}y+10xy^{2}

(iv) Given,

a^{3} + a^{2} + a – 3a + 5a^{2} – 9a^{3}

By combining the like terms,

=a^{3}-9a^{3}+a^{2}+5a^{2}+a-3a

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

Hence, By simplifying the like terms a^{3} + a^{2} + a – 3a + 5a^{2} – 9a^{3}= -8a^{3}+6a^{2}-2a.

(v) Given,

-8a^{3}b^{2} + 10a^{2}b^{3} – 8a^{3}b^{2} – 8a^{2}b^{3} + 5a^{3}b^{2}

By combining the like terms,

=-8a^{3}b^{2}-8a^{3}b^{2}+5a^{3}b^{2}+10a^{2}b^{3}-8a^{2}b^{3}

=-16a^{3}b^{2}+5a^{3}b^{2}+2a^{2}b^{3}

=-11a^{3}b^{2}+2a^{2}b^{3}

Hence, By simplifying the like terms -8a^{3}b^{2} + 10a^{2}b^{3} – 8a^{3}b^{2} – 8a^{2}b^{3} + 5a^{3}b^{2}=-11a^{3}b^{2}+2a^{2}b^{3}.

(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.