Question

How do you subtract `-2k^3 + k^2 - 9` from `5k^3 - 3k + 7`?

Answer 1

`= 7k^3- k^2 - 3k + 16`

Explanation:

Subtracting in Algebra is different from subtraction in arithmetic or in lower grades, where Subtracting always made the amount get less.
It was ALWAYS: Bigger - Smaller and the answer was smaller than what we started with with.

In Algebra, working with positive and negative numbers, throws that idea on its head.! This is why students find subtraction difficult!

KEY POINT: Any subtraction can be written as an ADDITION.

To SUBTRACT: - ADD on the INVERSE.

So `(8) color(red)- (color(blue)+5) = 3` can be written as `8 color(red)+ (color(blue)-5) = 3`

To make an inverse "change the sign"

If we write the question as an expression, there will be a minus sign between the two brackets: The minus will make the signs in the second bracket change.

`(5k^3 - 3k + 7)-(-2k^3 + k^2 -9)`

This can also be written as

`(5k^3 - 3k + 7) +(+2k^3 - k^2 +9) " add on the inverse"`

`= 5k^3 - 3k + 7 + 2k^3 - k^2 +9 " collect like terms"`

`= 7k^3- k^2 - 3k + 16`