Answer:
(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!!
