Question

How do you find the sum of `( 5x ^ { 3} + 3x ^ { 2} - 5x + 4)` and `( 8x ^ { 3} - 5x ^ { 2} + 8x + 9)`?

Answer 1

See the solution process below:

Explanation:

We can write the sum of these two terms as the expression:

`(5x^3 + 3x^2 - 5x + 4) + (8x^3 - 5x^2 + 8x + 9)`

We can find the sum by first removing all of the terms from parenthesis. Be careful to handle the signs of each individual term correctly:

`5x^3 + 3x^2 - 5x + 4 + 8x^3 - 5x^2 + 8x + 9`

Next, group like terms:

`5x^3 + 8x^3 + 3x^2 - 5x^2 - 5x + 8x + 4 + 9`

Now, combine like terms:

`(5 + 8)x^3 + (3 - 5)x^2 + (-5 + 8)x + (4 + 9)`

`13x^3 + (-2)x^2 + 3x + 13`

`13x^3 - 2x^2 + 3x + 13`

Answer 2

`(5x^3+3x^2−5x+4)+(8x^3−5x^2+8x+9)=`

`13x^3-2x^2+3x+13`

Explanation:

Remember you can only add common variables.
Like this,

`(5x^3+3x^2−5x+4)+(8x^3−5x^2+8x+9)`

`color(red)(5x^3)color(green)(+3x^2)color(blue)(−5x)+4color(red)(+8x^3)color(green)(−5x^2)color(blue)(+8x)+9`

Add and subtract the same colors
(See how they all have the same variables)

`color(red)(13x^3)color(green)(-2x^2)color(blue)(+3x)+13`

and you're done...

`(5x^3+3x^2−5x+4)+(8x^3−5x^2+8x+9)=`

`13x^3-2x^2+3x+13`