Expert: Abe Mantell - 8/13/2009

Question
Can you please help me with this, I'm confused. (step by step break downs would be great, if you could) Thank you very very much!

3.  Factor the following expressions using the method of common factors.

  (a)   6a+6c
  
  (b)   8x^2+2xb
  
  (c)   x^3y^2 +xy
     
4.  Factor the following differences of two squares.

  (a)   x^2-81

  (b)   t^2-4
  
  (c)   b^2-144
  

5.  Factor the following sums or differences of two cubes
       
       (a)   b^3-8

       (b)   x^3+8

       (c)   m^3-n^3

       (d)   c^3+f^3

Answer
Hello Amanda,

3.  Factor the following expressions using the method of common factors.

(a)   6a+6c, factor out the common factor "6" to get 6(a+c)

(b)   8x^2+2xb, factor out the common factor "2x" to get 2x(4x+b)

(c)   x^3y^2 +xy, common factor is "xy" ==> xy(x^2 y + 1)

4.  Factor the following differences of two squares.

(a)   x^2-81 = x^2 - 9^2 = (x+9)(x-9)

(b)   t^2-4 = t^2 - 2^2 = (t+2)(t-2)

(c)   b^2-144 = b^2 - 12^2 = (b+12)(b-12)


5.  Factor the following sums or differences of two cubes
REMEMBER: (a^3 + b^3) = (a+b)(a^2-ab+b^2) and (a^3 - b^3) = (a-b)(a^2+ab+b^2)
      
      (a)   b^3-8 = b^3 - 2^3 = (b-2)(b+2b+4)

      (b)   x^3+8 = x^3 + 2^3 = (x+2)(x^2-2x+4)

      (c)   m^3-n^3 = (m-n)(m^2+mn+n^2)

      (d)   c^3+f^3 = (c+f)(c^2-cf+f^2)

I hope this helps.

Abe