SIMPLIFYING ALGEBRAIC EXPRESSIONS WORKSHEET

Simplify the following algebraic expressions :

1)  4a + 2b + a

2)  x² + 3x + 2x + 5x²

3)  4a³ + 6a + 3a³ + 8a

4)  6x + 2(2x + 7)

5)  5n + 4(3n + 9)

6)  3(x + 2y) + 4(3x + y)

7)  3.2(x + y) + 2.3(x + y) + 4x

8)  3(4m + n) + 2m

9)  6(0.4f + 0.2g) + 0.5f

10)  3/4 + [(2/3) (s + 2t)] + s

11) (2/3)(y² - y - 3) + (1/3)(y² + 2y + 6)

12)  3[6a - 3(1 - a) - 5(a + 1)]

Answers

1. Answer :

 =  4a + 2b + a

=  4a + a + 2b

  =  5a + 2b

2. Answer :

=  x² + 3x + 2x + 5x²

=  x²  + 5x² + 3x + 2x

=  6x²  + 5x

3. Answer :

=  4a³ + 6a + 3a³ + 8a

=  4a³ + 3a³  + 6a + 8a

=  7a³ + 14a

4. Answer :

=  6x + 2(2x) + 2(7)

=  6x + 4x + 14

=  10x + 14

5. Answer :

=  5n + 4(3n) + 4(9)

=  5n + 12n + 36

=  15n + 36

6. Answer :

=  3(x + 2y) + 4(3x + y)

=  3(x) + 3(2y) + 4(3x) + 4(y)

=  3x + 6y + 12x + 4y

=  3x + 12x + 6y + 4y

=  15x + 10y

7. Answer :

=  3.2(x + y) + 2.3(x + y) + 4x

=  3.2(x) + 3.2(y) + 2.3(x) + 2.3 (y) + 4x

=  3.2 x + 3.2y + 2.3x + 2.3 y + 4x

=  3.2x  + 2.3x + 4x + 3.2y + 2.3y

=  9.5x + 5.5y 

8. Answer :

=  3(4m + n) + 2m

=  3(4m) + 3(n) + 2m

=  12m + 3n + 2m

=  14m + 3n

9. Answer :

=  6(0.4f + 0.2g) + 0.5f

=  6(0.4f) + 6(0.2g) + 0.5f

=  2.4f + 1.2g + 0.5f

=  2.4f + 0.5f + 1.2g 

=  2.9f + 1.2g 

10. Answer :

=  3/4 + [(2/3)(s + 2t)] + s

=  3/4 + [(2/3)(s) + (2/3)(2t)] + s

=  3/4 + 2s/3 + 4t/3 + s

=  3/4 + 2s/3 + s + 4t/3

=  3/4 + 2s/3 + 3s/3 + 4t/3

=  3/4 + (2s + 3s)/3 + 4t/3

=  3/4 + 5s/3 + 4t/3

11. Answer :

=  (2/3)(y² - y - 3) + (1/3)(y² + 2y + 6)

=  2y²/3 - 2y/3 - 6/3 + y²/3 + 2y/3 + 6/3

=  2y²/3 + y²/3 - 2y/3 + 2y/3 - 6/3 + 6/3

=  (2y² + y²)/3

=  3y²/3

=  y²

12. Answer :

=  3[6a - 3(1 - a) - 5(a + 1)]

=  3[6a - 3 + 3a - 5a - 5]

=  3[4a - 8]

=  12a - 24

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