Question

How do you combine like terms in `(2x^3-6x^2-7x-2)+(x^3+x^2+6x-12)`?

Answer 1

`3x^3-5x^2-x-14`

Explanation:

First get rid of the brackets.
Because there is a + sign between them, there will be no change at all, except we will have 8 terms and not just 2 terms.

Identify the like terms:

`color(red)(2x^3)color(blue)(-6x^2)color(lime)(-7x)color(magenta)(-2)color(red)(+x^3)color(blue)(+x^2)color(lime)(+6x)color(magenta)(-12)`

To begin with you might like to re-arrange the terms of the expression with the like terms together and with the powers in descending order. Later this will not be necessary.
Remember to keep the signs with the correct term.

=`color(red)(2x^3)color(red)(+x^3)color(blue)(-6x^2)color(blue)(+x^2)color(lime)(-7x)color(lime)(+6x)color(magenta)(-2)color(magenta)(-12)`

Now add the co-efficients, but the powers stay the same.
(Remember that `x` is actually `1x`)

=`color(red)(3x^3)color(blue)(-5x^2)color(lime)(-x)color(magenta)(-14)`