Question

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

Answer 1

`5x^4+4x^2`

Explanation:

You can ignore the parenthesis because they are adding.
If they were subtracting then all the terms inside the negative parenthesis would change sign.
So, let's rewrite it like this.

`2x ^ { 2} + 8x ^ { 4} + 2x ^ { 2} - 3x ^ { 4}`

Now just add and subtract common terms

`color(red)(2x ^ { 2}) color(green)(+8x ^ { 4} ) color(red)(+2x ^ { 2})color(green)( - 3x ^ { 4})`

`color(green)(5x^4)color(red)(+4x^2)`

Answer 2

`(2x^2+8x^4)+(2x^2-3x^4) = 5x^4+4x^2`

Explanation:

The first step is to clear the brackets. That will adjust the signs of the factors enclosed so the terms can be combined.

Given: `(2x^2+8x^4)+(2x^2-3x^4)`

Remove brackets and adjust signs:

`(2x^2+8x^4)+(2x^2-3x^4) = 2x^2+8x^4+2x^2-3x^4`

Notice that no signs had to be changed because both brackets were preceded by `+` signs.

Now we can arrange the terms:

`2x^2+8x^4+2x^2-3x^4 = 2x^2+2x^2+8x^4-3x^4`

Combining and re-arranging terms:

`2x^2+2x^2+8x^4-3x^4 = 4x^2+5x^4 = 5x^4+4x^2`