Factor y3 + 512 completely

(B=8)(y−8)⋅(y^2 +8y+64)

Step-by-step explanation:  

Changes made to your input should not affect the solution:

(1): "y3"   was replaced by   "y^3".

Factoring:  y3-512

Theory : A difference of two perfect cubes,  a3 - b3 can be factored into

             (a-b) • (a2 +ab +b2)

Proof :  (a-b)•(a2+ab+b2) =

           a3+a2b+ab2-ba2-b2a-b3 =

           a3+(a2b-ba2)+(ab2-b2a)-b3 =

           a3+0+0+b3 =

           a3+b3

Check :  512  is the cube of   8

Check :  y3 is the cube of   y1

Factorization is :

            (y - 8)  •  (y2 + 8y + 64)

Factoring  y2 + 8y + 64

The first term is,  y2  its coefficient is  1 .

The middle term is,  +8y  its coefficient is  8 .

The last term, "the constant", is  +64

Step-1 : Multiply the coefficient of the first term by the constant   1 • 64 = 64

Step-2 : Find two factors of  64  whose sum equals the coefficient of the middle term, which is   8 .

     -64    +    -1    =    -65

     -32    +    -2    =    -34

     -16    +    -4    =    -20

     -8    +    -8    =    -16

     -4    +    -16    =    -20

     -2    +    -32    =    -34

     -1    +    -64    =    -65

     1    +    64    =    65

     2    +    32    =    34

     4    +    16    =    20

     8    +    8    =    16

     16    +    4    =    20

     32    +    2    =    34

     64    +    1    =    65

Hope that helps!!

22 dimes and 9 nickels

step-by-step explanation: