Question

How do you simplify the sum `(8u^3+8u^2+6)+(4u^3-6u+3)`?

Answer 1

`12u^3 + 8u^2 - 6u + 9`

Explanation:

`(8u^3 + 8u^2 + 6) + (4u^3 - 6u + 3)`

We can remove the parenthesis since we are just adding:
`8u^3 + 8u^2 + 6 + 4u^3 - 6u + 3`

Now let's color-code the like terms which we will combine:
`color(red)(8u^3) quadcolor(green)(+quad8u^2) quadcolor(blue)(+quad6) quadcolor(red)(+quad4u^3) quadcolor(orange)(-quad6u) quadcolor(blue)(+quad3)`

`color(red)(12u^3) quadcolor(green)(+quad8u^2) quadcolor(blue)(+quad9) quadcolor(orange)(-quad6u)`

Now write it in descending degree (higher to lower exponent in variable, with just the number at the end)

`12u^3 + 8u^2 - 6u + 9`

Hope this helps!