Expert: Michael Tadesse - 9/17/2009

Question
2. Perform the indicated operation and simplify completely
    5x+5/5x+9 + 5x+13/5x+9
                                                                 
                                                   
     3.   Perform the indicated operation and simplify completely
  (x+11) (x-11)    

   

5. Factor 4x-40 completely              

6.   Perform the indicated operation and simplify completely
(x-2)²          

7.    factor x²+10x+21 completely        

8.   factor x² - 8x +16 completely           


9.   factor 4x²-9y²



10.   perform the indicated operation completely
(x+10) (x²+9x-8)    
     
11.    perform the indicated operation completely  
(x-3)³

Answer
Hello Laurie

Problem #2
You see that the denominators are the same, so you just add the numerators and put with the same denominator as before.

   5x+5 + 5x+13 = 10X + 18 = 2(5X + 9)
Now divide it by the denominator

2(5X + 9)/ 5x+9 = the expression cancels out and 2 will be the most simplified answer.



Problem #3

(x+11) (X-11)    

Just multiply the two polynomials and it is
X2 – 121 (its just multiplication)


Problem #5

To factor the equation, look out for common numbers or algebraic expressions everywhere.
Look, 4 is common for 4 and 40. X can’t be because it is only found in the first term.

4(X – 10)

Problem #6

In order to carry out this operation, you have to split it into two equal equations and multiply them

(X – 2) * (X – 2) = X2 - 4X + 4 (multiply and collect like terms)

Problem #7

To tackle this problem you have too look for two numbers of which their product is 21 and their sum is 10.

They are 7 and 3 aren’t they? Laurie
So the factored equation will be
(X +7) * (X + 3)



Problem #8

The same principle applies here.

Look for two numbers of which their product is 16 and their sum is -8

They are both -4

Therefore, (X – 4)*(X – 4) is the factored equation.

Problem #9

Now this is a little bit baffling, but simple if you observe it carefully. It is a product of two functions. You know that (a + b)(a – b) = a2 – b2

Following the above formula

4x²-9y² is the product of 2x +3y and 2x – 3y

(2x + 3y)*(2x – 3y)

Problem #10

Laurie, this is a matter of multiplying.
Carefully multiply each term in the bracket by every member of the equation in the other bracket.

X*( x²+9x-8) = X3 + 9X2 – 8X
10*( x²+9x-8) = 10X2 + 90X -80

Now collect like terms and add them

Finally you’ll get

X3 + 19X2 + 82X – 80

Final Problem

First find (X – 3)2 and multiply it by (X – 3)

Try it yourself and let me give you the answer

X3 – 3X2 – 9X + 27