How about factoring this one: x^3 + 8y^3?

Question

Could you explain how I could get the answer. Thanks guys!

Answer 1

formula is:

a^3 + b^3 = (a+b)(a^2 - ab + b^2), let's check
= a^2 - a^2b + ab^2 + a^2b - ab^2 + b^3, right!

your problem is: (x)^3 + (2y)^3, so use the formula with a = x, and b = 2y, or

x^3 + 8y^3 = (x+2y)(x^2 - x*2y + (2y)^2), clean this up.

Answer 2

we have the formula :
a^3 + b^3 = (a+b)(a^2 - ab + b^2)
and the problem is x^3 + 8y^3 = x^3 + (2y)^3
so with use the formula then
x^3 + 8y^3 = x^3 + (2y)^3
x^3 + 8y^3 = (x+2y)(x^2 - x*2y + (2y)^2)
x^3 + 8y^3 = (x+2y)(x^2 - 2xy + 4y^2)

Answer 3

Factor x³ + 8y³.
________

Notice that it is the sum of two perfect cubes. The sum of two perfect cubes can be factored as follows:

a³ + b³ = (a + b)(a² - ab + b²)

Now let
a = x
b = 2y

And we have:

x³ + 8y³ = x³ + (2y)³ = (x + 2y)(x² - x(2y) + (2y)²)

= (x + 2y)(x² - 2xy + 4y²)

Answer 4

First thing factor out to get it down to ^2 which will be.

(x + 2y)(x^2 + 4y^2) now factor (x^2 + 4y^2) which is as far as you can go just factoring. here is the reason why:

If you try (x + 2y)(x+2y) when you multply them back together you'll get.
x^2 + 4xy + 4y^2 wrong
If you try ( x - 2y)(x - 2y) when you multiply them back together you'll get.
x^2 - 4xy + 4y^2 wrong
If you try (x + 2y)(x-2y) when you multiply them back together you will get:
x^2 - 4y^2 signs wrong as you can see.
So just factoring your answer is going to be:
(x +y)(x^2 + 2y^2)

Answer 5

Use the formula a^3 + b^3 = (a + b)(a^b - ab + b^2)

your a = x and your b = 2y

Take it from here, is really easy.

Good Luck

Also try these:
http://search.freefind.com/find.html?id=5014414&pageid=r&mode=ALL&n=0&query=sum+of+two+cubes
http://www.purplemath.com/modules/specfact3.htm
http://www.purplemath.com/modules/specfact2.htm

Answer 6

x^3 + 8y^3
= x^3 + (2x)^3
= (x + 2y)^3 -- 3x(2y)(x + 2y)
= (x + 2y){(x + 2y)^2 -- 3x(2y)}
= (x + 2y){x^2 + 4xy + 4y^2 -- 6xy}
= (x + 2y)(x^2 -- 2xy + 4y^2)