Question

Find the greatest common factor. 2y^3, 8y

Answer 1

Answer:

STEP1:Equation at the end of step 1

2y3 - 8y

STEP2:

STEP3:Pulling out like terms

 3.1     Pull out like factors :

   2y3 - 8y  =   2y • (y2 - 4) 

Trying to factor as a Difference of Squares:

 3.2      Factoring:  y2 - 4 

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 : 4 is the square of 2

Check :  y2  is the square of  y1 

Factorization is :       (y + 2)  •  (y - 2) 

Final result :

2y • (y + 2) • (y - 2)