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Factor y3 + 512 completely

1 Answer

3 votes

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!!

User Don Li
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