ALGEBRAIC

1. Determine the coefficients of p in each of the following algebraic expression !

a. – 3 p² + 8p

b. 4p² – p

c. 2p² – 5pq – 4p

d. p³ – 8p² + p

2. Write the like terms in each of the following algebraic expressions !

a. 7x + 2y – 9x

b. 4a + 5ab – 7a² – 16ab + 8a

c. 5p² + 4p + 3 + 3p² – 5p – 7

3. Work out each of the following multiplications of algebraic expressions !

a. 4 ´ 2 ´ a ´ b

b. -2 ´ (-3q) ´ (-4p)

c. 7kn ´ 2m²n ´ (-3 km)

4. Work out each of the following exponentiations of algebraic expressions !

a. (12k)²

b. (-ab)⁴

c. (4p²)³

d. (-5y²)³

e. (2p ´ 5q)⁴

f. (2p² ´ pq)³

5. Work out each of the following divisions of algebraic expressions !

a. abc : ac

b. 12a² : 6a

c. 6x⁸y⁵ : 3x²y³

d. 8x²y²z² : 4x³y²z²

e. 27a⁶b⁵c⁴ : 3a²b³c : 9a³bc²

f. 48p⁵q⁸r⁶ : (-6p²q³r³) : 4pq²r²

6. Simplify !

a. 8a + 4a

b. 7a + 5b – 2a

c. 5x + 7y – 3x – 2y

d. 7x2 – 4x2 3y – 6y

7. Simplify !

a. 4(39 + 2) – 6p

b. 10p – (3 – 2p)

c. 5(x – 2y) – 3(2x – y)

d. -3(x – 4y) + 4(5x – 3y)

8. Find the sun of :

a. 6a + 7 and 2a – 4

b. –x² + 5xy and 4x² – 4xy

c. 5x – 2xy + 6y and -4 + 3xy – 5y

d. -2p³ + 3p² – 4p and 2p³ – p2 + p

9. Subtract !

a. 2a – 5 from 8a + 4

b. -3a² – 9a from a² + 5a

c. 4x² + 2x – 7 from x² + 3x + 2

d. 5x² – xy – 2y² from 8x² + 4xy + y²

10. Find the value of each of the following algebraic expressions if k = 4 !

a. 3k

b. -5k

c. 2k – 9

d. -3k² + k

e. k³ + 2k²

f. 3k² + 5k – 8

11. Find the value of each of the following algebraic expressions !

a. 2q + 7 if q = - 5

b. 2p + 3pq if p = 5 and q = -4

c. 2m² – 3mn if m = -7 and n = 8

d. x³ – y² if x = -4 and y = 9

12. If a = -3, b = 1 and c = -5, find value of each of the following algebraic expressions !

a. 2ab + 3bc – 4ac

b. (2ab – c²)²

c. ab² – bc² – ac²

d. 2a³ + 3b⁴ – 4c²

13. A motorcycle moved at a speed (v) of 60 km/hour for 1 hour and 45 minutes

a. Write a formula which expresses the relation between the distance (s) traveled and the time (t) taken and speed (v) !

b. Find the distance traveled by the motorcycle !

14. Find the LCM of each of the following pairs of algebraic expressions !

a. 6ab and 18a

b. 18a²b and 24abc

c. 10a²b³c and 15b²c²d

d. 10pqr, 15pqr², and 20p²q²r²

e. 8pq², 24qr², and 12p³qr

f. 15p²q³r, 6q²rs, and 10pq²rs³

15. Find the GCD of each of the following pairs of algebraic expressions !

a. 9ab and 12 bc

b. 18a²bc and 12ab²

c. 16ab²c and 20b²c²d

d. 15pq², 25qr³, and 70pqr

e. 18p²qr², 27p³q²r, and 45pqr³

f. 24p²q²r, 32pq²s, and 72q³r²s³