mathematics

[keirah]

is there a general rule for the subtraction of powers/indices? for example the difference between 4 cubed minus 4 squared

thanks

[Gef]

I don't think there is a general rule or formula. You just have to work it out the long way, ie 4 cubed minus 4 squared is 64 minus 16.

[tony1941]

Yes, it's floating point arithmetic. For addition and subtraction, the exponents - or powers - of the numbers have to match. In your example, the method is to write 4^4 (4 to the power 4) as 4*4^3; then when you add this to 4^3 (4 cubed), you get 5*4^3. This is a bad example for seeing the generality, but if you are considering numbers like 2.7*10^3 and 1.9*10^5, then the process comes down to moving the decimal point in each mantissa (the numbers 2.7 and 1.9 in this case) so that the powers of 10 coincide. ie. (1.9+0.027)*10^5=1.927*10^5

[Buenchico]

I'm not too sure what you mean by a 'general rule' in this case but, from the example you've given(by taking factors), you get this:
4 cubed - 4 squared = 4 squared x (4 - 1)

Generalising;
x cubed - x squared = x sqared x (x - 1)

Chris

[Buenchico]

I've just realised that using ' x ' to represent a number and to represent 'multiplied by' in the same line of my answer, might look a little confusing! I'll write that again (and choose a different letter!):

Generalising:
(y cubed) minus (y squared) = (y squared) multiplied by ( y minus 1).

Chris