Question

How do you evaluate `(5x ^ { 4} - 6x ^ { 3} + 4x ^ { 2} + 6x ) + ( - 10x ^ { 3} + 9x ^ { 2} + 10x - 8)`?

Answer 1

`5x^4-16x^3+13x^2-4x-8`

Explanation:

First, just drop the parentheses:

`color(red)(5x^4)-color(orange)(6x^3)+color(green)(4x^2)+color(blue)(6x)-color(orange)(10x^3)+color(green)(9x^2)+color(blue)(10x)-color(magenta)(8)`

Now, we can rearrange the expression using the commutative to put like terms next to each other:

`color(red)(5x^4)-color(orange)(6x^3)-color(orange)(10x^3)+color(green)(4x^2)+color(green)(9x^2)+color(blue)(6x)-color(blue)(10x)-color(magenta)(8)`

Finally, combine like terms:

`color(red)(5x^4)-color(orange)(16x^3)+color(green)(13x^2)-color(blue)(4x)-color(magenta)(8)`