Question

How do you combine `(-2t^4+6t^2+5)-(-2t^4+5t^2+1)`?

Answer 1

Group and combine terms with equivalent powers of `t` to get:
`color(white)("XXXX")` `t^2+4`

Explanation:

`(color(red)(−2t^4)color(blue)(+6t^2)color(green)(+5))−(color(red)(−2t^4)color(blue)(+5t^2)color(green)(+1))`

`color(white)("XXXX")`Possibly easier (and less error prone) if we change the main subtraction to addition:
`=(color(red)(−2t^4)color(blue)(+6t^2)color(green)(+5))+(color(red)(2t^4)color(blue)(-5t^2)color(green)(-1))`

`color(white)("XXXX")`Group by powers of `t`
`= color(red)(-2t^4 + 2t^4)color(blue)(+6t^2-5t^2)color(green)(+5-1)`

`color(white)("XXXX")`Combine terms with equal powers of "t"
`= color(red)(0)color(blue)(+1t^2)color(green)(+4)`