Practice the questions given in the Worksheet on Addition of Unlike Terms and know various models of questions framed on the topic. Unlike Like Terms, we can’t add them together to obtain a single sum result. Explore all the problems on adding unlike fractions over here and know how to add unlike terms in an algebraic expression.

Get to know the step-by-step explanation while solving the questions on the addition of unlike terms. Students can make the most out of the Printable Math Addition of Unlike Terms Worksheet PDF to have a strong conceptual base on simplifying algebraic expressions.

Read Similar Articles: Worksheet on Subtraction of Unlike Terms

### Addition of Unlike Terms Worksheet with Answers

**I. Find the sum of:
**(i) 6x and 3y

(ii) 5b and 4b

^{2}

(iii) 7y

^{2}z and 2y

^{2}

(iv) 4xy, 2x and 5y

(v) 2p, 5p

^{2}and 9p

^{3}

(vi) mn, np, and pm

**Solution:**

(i) Given 6x and 3y

The sum of 6x and 3y is 6x+3y.

(ii) Given 5b and 4b^{2
}The sum of 5b and 4b^{2} is 5b+4b^{2}

(iii) Given 7y^{2}z and 2y^{2}

The sum of 7y^{2}z and 2y^{2} is 7y^{2}z + 2y^{2}

(iv) Given 4xy, 2x and 5y

The sum of 4xy, 2x and 5y is 4xy+2x+5y.

(v) Given 2p, 5p^{2} and 9p^{3}

The sum of 2p, 5p^{2} and 9p^{3} is 2p + 5p^{2}+9p^{3}

(vi) Given mn, np, and pm

The sum of mn, np, and pm is mn+np+pm.

**II. Simplify the following:
**(i) -2x and 8y

(ii) 6c and -3b

(iii) -y

^{2}and y

(iv) ab and -bc

(v) –XYZ and XY

(vi) a

^{2}b and –ab

^{2}

**Solution:**

(i) Given, -2x and 8y

Add the given unlike terms,

=-2x+8y

Hence, the sum of unlike terms -2x and 8y is -2x+8y.

(ii) Given, 6c and -3b

Add the given unlike terms,

=6c+(-3b)

=6c-3b

Hence, the sum of unlike terms 6c and -3b is 6c-3b.

(iii) Given, -y^{2} and y

Add the given unlike terms,

= -y^{2} +y

Hence, the sum of unlike terms -y^{2} and y is -y^{2} +y.

(iv) Given, ab and -bc

Add the given unlike terms,

=ab+(-bc)

=ab-bc

Hence, the sum of unlike terms ab and -bc is ab-bc.

(v) Given, –XYZ and XY

Add the given unlike terms,

=-XYZ+XY

Hence, the sum of unlike terms –XYZ and XY is -XYZ+XY.

(vi) Given, a^{2}b and –ab^{2}

Add the given unlike terms,

=a^{2}b+(-ab^{2})

=a^{2}b -ab^{2}

Hence, the sum of unlike terms a^{2}b -ab^{2}.

**
III. Add the following:
**(i) m, 5m and 4n

(ii) 3p, 5p and 6pq

(iii) 2b, 7c and 8c

(iv) 4mn, 3nm and 9n

(v) 20xy, 16yx and 18xz

(vi) 8a

^{2}b, 4ab and 6ba

^{2}

**Solution:**

(i) Given, m, 5m and 4n

Add the unlike terms,

=m+5m+4n

=6m+4n

Therefore, By adding m, 5m and 4n we get 6m+4n.

(ii) Given, 3p, 5p and 6pq

Add the unlike terms,

=3p+5p+6pq

=8p+6pq

Therefore, by adding 3p, 5p and 6pq is 8p+6pq.

(iii) Given, 2b, 7c and 8c

Add the unlike terms,

=2b+7c+8c

=2b+15c

Therefore, by adding 2b+7c+8c we get 2b+15c.

(iv) Given, 4mn, 3nm and 9n

Add the unlike terms,

=4mn+ 3nm+ 9n

=7mn+9n

Therefore, by adding 4mn+3nm+ 9n we get 7mn+9n.

(v) Given, 20xy, 16yx and 18xz

Add the unlike terms,

=20xy+ 16yx + 18xz

=36xy+18xz

Therefore, by adding 20xy, 16yx, and 18xz we get 36xy+18xz.

(vi) Given, 8a^{2}b, 4ab and 6ba^{2}

Add the unlike terms,

=8a^{2}b+4ab+6ba^{2}

=14a^{2}b+4ab

Therefore, by adding 8a^{2}b, 4ab and 6ba^{2} we get 14a^{2}b+4ab.

**Iv. Evaluate the following by arranging the unlike terms together:
**(i) 8x – 2y – 4x

(ii) 15mn – 7mn + 4np

(iii) a – 8a + 4b + 7a

(iv) 14x + 2y – 4x – y

(v) 2xy + 4yx + 18

(vi) 7abc – 10ab + 12abc

**Solution:**

(i) Given, 8x – 2y – 4x

By arranging the unlike terms together,

=8x-4x-2y

=4x-2y

Hence, By evaluating 8x – 2y – 4x is 4x-2y.

(ii) Given, 15mn + 4np – 7mn

By arranging the unlike terms together,

=15mn-7mn+4np

=7mn+4np

Hence, By evaluating 15mn + 4np – 7mn is 15mn + 4np – 7mn.

(iii) Given, a – 8a + 4b + 7a

By arranging the unlike terms together,

=a – 8a + 7a + 4b

=8a-8a+4b

=4b

Hence, By evaluating a – 8a + 4b + 7a is 4b.

(iv) Given, 14x + 2y – 4x – y

By arranging the unlike terms together,

=14x-4x+2y-y

=10x+y

Hence, By evaluating 14x + 2y – 4x – y is 10x+y.

(v) Given,2xy + 4yx + 18-xy

By arranging the unlike terms together,

=2xy-xy+4yx+18

=xy+4yx+18

=5yx+18

Hence, By evaluating 2xy + 4yx + 18-xy is 5yx+18.

(vi)Given, 7abc – 10ab + 12abc

By arranging the unlike terms together,

=7abc+12abc-10ab

=19abc-10ab

Hence, By evaluating 7abc – 10ab + 12abc is 19abc-10ab.

**V. **Sameera bought m apples and n oranges from the fruit market. How many fruits did she buy altogether?

**Solution:**

Given,**
**Sameera bought apples=m

Sameera bought oranges=n

Total no. of fruits bought by Sameera=m+n.

Hence, Sameera bought m+n fruits from the market.

**VI. **Mahesh scored X marks in Maths and Y marks in science. How many marks did he score altogether in two subjects?

**Solution:**

Given,

Mahesh scored marks in Maths=X

Mahesh scored marks in Science=Y

Mahesh scored marks in both the subjects=X+Y.

Therefore, Mahesh scored X+Y marks in both subjects.

**VII. **Sarath walked X km on Friday and Y km on Saturday. How many km did he run on both days?

**Solution:**

Given,

No. of Km Sarath walked on Friday=X km

No. of km Sarath walked on Saturday=Y km

No. of km Sarath walked on both the days=X+Y.