Sum of 2 cubes

[Bladesofhalo]

I have the problem:
8x^3 + 125y^3

I have to express it as the sum of 2 cubes, which i have done
2(x)^3 + (5y)^3 = (2x+5y)(4x^2 - 2x5y + 25y)

Now i need to multiply the section in bold so that I can get the problem i started off with(shown in italics). But I get confused when I begin multiplying the variables and such. Can someone show me how to multiply it correctly so that I end up with the problem in italics?

 

[Denis]

I have the problem:
8x^3 + 125y^3

I have to express it as the sum of 2 cubes, which i have done
2(x)^3 + (5y)^3 = (2x+5y)(4x^2 - 2x5y + 25y)

Now i need to multiply the section in bold so that I can get the problem i started off with(shown in italics). But I get confused when I begin multiplying the variables and such. Can someone show me how to multiply it correctly so that I end up with the problem in italics?

Nope, nobody can, cause the section in bold is incorrect :shock:

 

[Bladesofhalo]

You kiddin?
Heres what my book says in the crappy detail

Sum of 2 Cubes
a^3 + b^3= (a + b)(a^2 - ab + b^2)

So 8x^3 + 125y^3
(2x)^3 + (5y)^3 = (2x+5y)(4x^2 - 2x5y + 25y^2)

Was it the 25y^2 that was wrong? I could only spot that mistake.[/b]

 

[Denis]

Yes; you showed 25y; also, 2x5y threw me: USUAL to show 10xy.
So we have:
(2x+5y)(4x^2 - 10xy + 25y^2)

Multiply what's in right brackets by 2x, then by 5y:
2x times (4x^2 - 10xy + 25y^2) = 8x^3 - 20x^2y + 50xy^2
5y times (4x^2 - 10xy + 25y^2) = 20x^2y - 50xy^2 + 125y^3

Add 'em up:
8x^3 - 20x^2y + 50xy^2 + 20x^2y - 50xy^2 + 125y^3 = 8x^3 + 125y^3

G'nite.