**Introduction to advance algebra ii:**

Algebra ii is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures. Together with geometry, analysis, topology, combinatory, and number theory, algebra is one of the main branches of pure mathematics. (Source: Wikipedia)

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**Advance algebra ii - Example: 1**

** ** Solve the equation by using the factorization method x^{2}+5x+6=0

**Solution:**

x^{2}+14x+48=0

x^{2}+6x+8x+48=0

x(x+6) +8(x+6) = 0

(x+6)(x+8)=0

x+6=0 and x+8=0

x+6-6=0-6 and x+8-8=0-8

**x=-6 and x=-8**

Therefore, x = {-6,-8}

**Answer: x _{1} = -6 and x_{2} = -8**

**Advance algebra ii - Example: 2**

Simplify 7a^{3} + 91a

**Solution:**

** ** 7a^{3} + 91a

We will take the 7a as common from 7a^{3} and 91a

Then the expression become as,

7a (a^{2} + 13)

**Answer: 5a ^{2} + 60a = 7a (a^{2} + 13)**

**Advance algebra ii - Example: 3**

** ** Simplify 22(y+6) +8y(y+6)

**Solution:**

22(y+6) +8y(y+6)

Here we can take y+6 as common from both 22(y+6) and 8y(y+6)

Then the expression become as,

(y+6)(22+8y)

**Answer: 9(y-2) +6y(y-2) = (y+6) (22 + 8y)**

**Advance algebra ii - Example: 4**

If c= -3 and d=5. Then what is –c^{3}d^{2}?

**Solution:**

-c^{3}d^{2}

Plug x=-3 and y=2 in the given expression

-((-3)^{3} * (5)^{2})

-((-3*-3*-3) * (5*5))

-(-27 * 25)

-675

**Answer: -c ^{3}d^{2} = -675**

**Advance algebra ii - Example: 5**

Solve 11 + b ≤ 19 and b/7 ≥ -1

**Solution:**

Take 11 + b ≤ 19

Subtract by 11 on both sides,

11 - 11 + b ≤ 19 – 11

b ≤ 8.

Take b/7 ≥ -1

Multiply by 3 on both sides,

b/7 * 7 ≥ -1 * 7

b ≥ -7

Therefore, the final solution is

-7 ≤ b ≤ 7

Please browse expert math related websites for more help on Basic Arithmetic
Fractions.

**1) ** Solve 48 + b ≤ 8 and b/7 ≥ -1

**Answer: 48 + b ≤ 8 and b/7 ≥ -1 = -7 ≤ b ≤ 7**

**2) ** Simplify 56(y-9) -51y(y-9)

**Answer:** **56(y-9) -51y(y-9)= (y - 9) (56-51y)**

**3)** Simplify 6a^{3} + 8a

**Answer: 6a ^{3} + 8a= 2a(3a^{2}+4)**

**4)** Solve the equation by using the factorization method x^{2}+15x+54=0

**Answer: x _{1} = -6 and x_{2} = -9**

**5)** If l=-1 and m=5. Then what is l^{4}m^{2}?

**Answer: l ^{4}m^{2} = -25**