help with my maths?

Question

A friend gave me this rule for my maths homework because I couldn't work it out (I wont bore you with everything else.)
The rule is n^3-m^3=(n-m)(n^2+m^2+nm) . The main problem I have is I don't know what to do here: m)(n and nm (is it added together or times or???)Can someone please give an example or an explanation of how to use it.

Answer 1

n and m are two seperate numbers nm is those two numbers multiplied together like if you had
8 and 5 for m and n then MN would be 40 cause it is m times n is 8 times 5 which is 40

Answer 2

Ok

The rule is correct. Let' show the proof

n^3-m^3= (n-m)(n^2+m^2+nm) (use FOIL)

= n^3 +nm^2 +n^2m -mn^2 -m^3 -nm^2

= n^3 -m^3 (see the other terms cancel)

Hope that helps.

Answer 3

What this is a factoring formula. to simplify it can be rewritten as:

(n3-M3)= (n-m)X(n2+nm+m2)
Let suppose n=3 and m=2
then plug these values;

Left side = (3X3X3)-(2X2X2)
=27-8
=19

Right side=
(3X3) + (2X2)+2X3
=9+4+6
=19
Thus Right side= Left side

I hope this helps you.

Answer 4

mn means m and n are multiplied together. the formula tells you how to factor a sum or difference of cubes, such as
x³ - 64 = (x - 4)(x² + 4x + 16)
8x³ + 1 = (2x + 1)(4x² - 2x + 1)

Answer 5

n^3-m^3=(n-m)*(n^2+m^2+n*m)

if you have (x^3-1)/(x-1)
so you can simplify the equation by using this formula
(x-1)*(x^2+1+x)/(x-1)=X^2+x+1

the same formula is :

n^3+m^3=(m+n)*(n^2+m^2-m*n)