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 y2(q-4)-c(q-4) Final result : (q - 4) • (y2 - c)

Step by step solution :Step  1  :Equation at the end of step  1  : ((y2) • (q - 4)) - c • (q - 4) Step  2  :Equation at the end of step  2  : y2 • (q - 4) - c • (q - 4) Step  3  :Pulling out like terms :

 3.1      Pull out     q-4 

After pulling out, we are left with : 
      (q-4) • ( y2  *  1 +( c  *  (-1) ))

Trying to factor as a Difference of Squares :

 3.2      Factoring:  y2-c 

Theory : A difference of two perfect squares,  A2 - B2  can be factored into  (A+B) • (A-B)

Proof :  (A+B) • (A-B) =
         A2 - AB + BA - B2 =
         A2 - AB + AB - B2 = 
         A2 - B2

Note :  AB = BA is the commutative property of multiplication. 

Note :  - AB + AB equals zero and is therefore eliminated from the expression.

Check :  y2  is the square of  y1 

Check :  c1   is not a square !! 
Ruling : Binomial can not be factored as the difference of two perfect squares

Final result : (q - 4) • (y2 - c)

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