Question

How do you combine like terms in `(8x + 6x ^ { 3} - 2x ^ { 2} ) - ( x ^ { 4} - 8x ^ { 3} + x )`?

Answer 1

`-x^4+14x^3-2x^2+7x`

Explanation:

Each term with similar power can be combined

i.e. `(color(red)(8x)+color(green)(6x^3)-color(blue)(2x^2))-(x^4-color(green)(8x^3)+color(red)x)`

Distribute the negative

`color(red)(8x)color(green)(+6x^3)color(blue)(-2x^2)-x^4color(green)(+8x^3)color(red)(-x)`

`color(red)(8x-x)color(green)(+6x^3+8x^3)color(blue)(-2x^2)-x^4`

`color(red)(7x)color(green)(+14x^3)color(blue)(-2x^2)-x^4`

Rearrange the expression according to the exponents (from highest to lowest)

`-x^4color(green)(+14x^3)color(blue)(-2x^2)color(red)(+7x)`