SIMPLIFYING ALGEBRAIC EXPRESSIONS PRACTICE PROBLEMS

To simplify algebraic expression, first we have to be clear with like and unlike terms.

Like Terms :

Like terms are terms that have the same variables with the same exponents.

Terms that are not like terms in unknown as unlike terms.

Let us assume

Day 1

Day 2

a = 1 kg of potato

b1 kg of onion

c = 1 kg of tomatoes

d = 1 kg of lady fingers

3a

7b

8c

0d

4a

0b

2c

3d

(3a + 4a) + (7b + 0b) + (8c + 2c) + (0d + 3d)

=  7a 7b + 10c + 3d

So, 7 kg of potatoes, 7 kg of onion, 10 kg of tomatoes and 3 kg of lady fingers.

Simplify the following expression :

Problem 1 :

 3x2 – x + 6 + x2 + 3x

Solution :

=  3x2 – x + 6 + x2 + 3x

By grouping the like terms, we get

(3x2 + x2) + (3x – x) + 6

By combining the like terms, we get

=  4x2 + 2x + 6

Problem 2 :

 2a – 3b + 4 – a + 1

Solution :

=  2a – 3b + 4 – a + 1

By grouping the like terms, we get

(2a – a) – 3b + (4 + 1)

By combining the like terms, we get

=  a – 3b + 5

Problem 3 :

2c – c2 + 3c + 1

Solution :

=  2c – c2 + 3c + 1

By grouping the like terms, we get

(2c + 3c) – c2 + 1

By combining the like terms, we get

=  -c2 + 5c + 1

Problem 4 :

2c + cd – 4c + dc – 4d

Solution :

=  2c + cd – 4c + dc – 4d

(2c – 4c) + (cd + dc) – 4d

=  2cd – 2c – 4d

Problem 6 :

5x – 10y + 6x

Solution :

=  5x – 10y + 6x

(5x + 6x) – 10y

=  11x – 10y

Problem 7 :

5 – m + 5r – m

Solution :

=  5 – m + 5r – m

=  5r -m -m + 5

=  5r – 2m + 5

Problem 8 :

6ac + 6a – 4c 

Solution :

=  6ac + 6a – 4c

There is no like terms.

Problem 9 :

7e - 8f – 2e + 5f

Solution :

=  7e - 8f – 2e + 5f

(7e – 2e) + (5f-8f)

=  5e – 3f

Problem 10 :

8x · 5

Solution :

=  8x · 5

=  40x

Problem 11 :

(a – c) x 7

Solution :

=  (a – c) · 7

=  7a – 7c

Problem 12 :

3 x a x a x b x b x b

Solution :

=  3 x a x a x b x b x b

a is repeated 2 times and b is repeated 3 times.

=  3a2b3

Problem 13 :

2 · x + x · x + x · x · x

Solution :

2 · x + x · x + x · x · x

=  2x + x2 + x3

Problem 14 :

2x2 x 3x

Solution :

=  2x2 x 3x

=  6x3

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