Question

Perform the indicated operation (7x4 + 11x3 – x2 – 8x + 6) – (-12x4 + 9x2 – 15)

Answer 1

Combine like terms.
Like terms have the same variable raised to the same power.
7x^4 + 12x^4 = 19x^4
11x^3
-x^2 - 9x^2 = -10x^2
-8x
6 + 15 = 21
19x^4 + 11x^3 -10x^2 -8x + 21

Answer 2

`19x^4 + 11x^3 - 10x^2 - 8x + 21`

Explanation:

We have the expression:

`(7x^4 + 11x^3 - x^2 - 8x + 6) - (-12x^4 + 9x^2 - 15)`

The first step is to apply the indicated subtraction, respecting the law of signs.

`7x^4 + 11x^3 - x^2 - 8x + 6 +12x^4 - 9x^2 + 15`

Now we put together like terms (those that have the same variable with the same exponent).

adding
`7x^4` and
`12x^4`

`19x^4 + 11x^3 - x^2 - 8x + 6 - 9x^2 + 15`

adding
`-x^2` and
`-9x^2`

`19x^4 + 11x^3 - 10x^2 - 8x + 6 + 15`

and adding
`+6` and
`+15`

`19x^4 + 11x^3 - 10x^2 - 8x + 21`

the answer is:

`19x^4 + 11x^3 - 10x^2 - 8x + 21`