Solution - Other Factorizations

Reformatting the input :

Changes made to your input should not affect the solution:

 (1): "q2"   was replaced by   "q^2". 

Step  1  :

Equation at the end of step  1  :

  1 -  (22•52q2)

Step  2  :

Trying to factor as a Difference of Squares :

 2.1      Factoring:  1-100q² 

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 :  1  is the square of  1 
Check : 100 is the square of 10
Check :  q²  is the square of  q¹ 

Factorization is :       (1 + 10q)  •  (1 - 10q) 

Final result :

  (10q + 1) • (1 - 10q)