Question

18y^3-33y^2+2y+5 factor​

Answer 1

Step-by-step explanation:

2y5-18y3 

Final result :

2y3 • (y + 3) • (y - 3)

Step by step solution :

Step  1  :

Equation at the end of step  1  :

(2 • (y5)) - (2•32y3)

Step  2  :

Equation at the end of step  2  :

2y5 - (2•32y3)

Step  3  :

Step  4  :

Pulling out like terms :

 4.1     Pull out like factors :

   2y5 - 18y3  =   2y3 • (y2 - 9) 

Trying to factor as a Difference of Squares :

 4.2      Factoring:  y2 - 9 

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 : 9 is the square of 3

Check :  y2  is the square of  y1 

Factorization is :       (y + 3)  •  (y - 3) 

Final result :

2y3 • (y + 3) • (y - 3)