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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Example problems for advance algebra ii :

 

Advance algebra ii - Example: 1

   Solve the equation by using the factorization method x2+5x+6=0

Solution:

   x2+14x+48=0

   x2+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: x1 = -6 and x2 = -8

Advance algebra ii - Example: 2

  Simplify 7a3 + 91a

Solution:

  7a3 + 91a

We will take the 7a as common from 7a3 and 91a

Then the expression become as,

  7a (a2 + 13)

Answer: 5a2 + 60a = 7a (a2 + 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 –c3d2?

Solution:

  -c3d2

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

  -((-3)3 * (5)2)

  -((-3*-3*-3) * (5*5))

  -(-27 * 25)

  -675

Answer: -c3d2 = -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

 

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Practice problems for advance algebra ii -:

 

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 6a3 + 8a

Answer: 6a3 + 8a= 2a(3a2+4)

4) Solve the equation by using the factorization method x2+15x+54=0

Answer: x1 = -6 and x2 = -9

5)   If l=-1 and m=5. Then what is l4m2?

Answer: l4m2 = -25