Question

How do you combine like terms in `(9x ^ { 5} - 7x ^ { 3} + x ) + ( 6x ^ { 4} + 9x ^ { 3} )`?

Answer 1

It's addition, so the brackets are not needed. So, in order to combine like terms, we simply add the coefficients of terms with the same exponent.

Explanation:

In this case:

`(9x ^ 5 - 7x ^ 3 + x ) + ( 6x ^4 + 9x^3) =9x ^ { 5} - 7x ^ { 3} + x + 6x ^ { 4} + 9x ^ { 3}`

There are only two terms with the same exponent, `- 7x ^ 3` and `9x ^ { 3}`, so we can combine these two only.

`-7+9=2`, so the new term is `2x^3`

`(9x ^ 5 - 7x ^ 3 + x ) + ( 6x ^4 + 9x^3) = 9x^2+6x^4 +2x^3+x`

Another thing to note is that when we write equations, we list the terms in decreasing order of exponent.