ALGEBRAIC
1. Simplify each of the following algebraic fractions !
a. 
b. 
c. 
d. 
2. By finding the common denominator, simplify the following algebraic expressions !
a. 
b. 
c. 
d. 
e. 
f. 
g. 
h. 
3. By finding the common denominator, simplify the following algebraic expressions !
a. 
b. 
4. Find the LCM of the denominators of the following algebraic fractions, and then simplify !
a. 
b. 
c. 
d. 
5. Simplify the following algebraic fractions !
a. 
b. 
c. 
d. 
e. 
f. 
g. 
h. 
6. Simplify the following algebraic fractions !
a. 
b. 
c. 
d. 
e. 
f. 
g. 
h. 
7. Find the power of each of the following algebraic exponentiations !
a. 
b. 
c. 
d. 
e. 
f. 
8. Find the product quotient of each of the following algebraic multiplications divisions !
a. 
b. 
c. 
d. 
e. 
9. Expand the following algebraic expressions !
a. x(2x + 5
b. 3x(x – 2)
c. -3x2(6x + 5xy)
d. 5p(2p – 3q + 4)
e. 4p2(3p2 – 5pq + 6q2)
10. Expand by means of the distributive law !
a. (x + 3) (x + 4)
b. (x + 2) (x – 5)
c. (3x + 2y) (x – 5y)
d. (3x – 4y) (2x + 7y)
e. (4x – 3y) (5x – 4y)
11. Expand the following algebraic expressions using schemes !
a. (a + 3) (a + 5)
b. (3a + 4) (3a – 2)
c. (4x – 2y) (4x – 5y)
d. (1 – 4y) (1 + 4y)
e. (9 + 12y) (9 – 12y)
f. (x2 + y2) (x2 – y2)
g. (x2 + 5x) (x2 – 10x)
h. (p + 3) (p2 – 2p + 1)
i. (p – 4) (p2 + 4p + 16)
j. (3p + 2q) (9p2 – 6pq + 4q2)
12. Expand the following squared binomials !
a. (m + n)2
b. (a – 10)2
c. (4p + 15)2
d. (3p – 10)2
13. Copy and then fill in the blanks !
a. (x + …)2 = … + … + 16
b. (3x - … )2 = … - … + 25
c. (3y + … )2 = … + 24y + …
d. (4y - ….)2 = … - 40y + …
14. Expand the following algebraic expressions and simplify the results !
a. 
b. 
c. 
d. 
e. 
f. 
g. 
h. 
15. By using identity a(b ++c) or (x +a) (x – a), do the following multiplications !
a. 9 ´ 76
b. 7 ´ 89
c. 6 ´ 94
d. 4 ´ 236
e. 7 ´ 324
f. 5 ´ 468
g. 32 ´ 28
h. 75 ´ 85
i. 43 ´ 37
j. 38 ´ 32
k. 76 ´ 74
l. 91 ´ 109
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