**Q: Add: (3x**^{3}+2x^{2}-5x) + (-4x^{3}-x^{2}-8x)

A: Here we are just asked to clean things up and combine like terms: basically, add apples with apples and oranges with oranges, but don’t accidentally add apples with oranges!

x^{3} terms get added with x^{3} terms

x^{2} terms get added with x^{2} terms

x terms get added with other x terms

So, let’s use color to highlight the like terms:

**(3x**^{3}+2x^{2}-5x) + (-4x^{3}–x^{2}-8x)

How many total **x**^{3} terms do you have? **3x**^{3}+ -4x^{3} = -1**x**^{3}

How many total **x**^{2} terms do you have? **2x**^{2}+**–x**^{2 }= 1**x**^{2}

How many total **x** terms do you have? **-5x**+ **-8x = -13x**

Did we forget anyone? Did anyone not have a match that we need to bring along? Nope! Everyone from both sets of parentheses is accounted for!

So, final answer:

**(3x**^{3}+2x^{2}-5x) + (-4x^{3}–x^{2}-8x) = -1**x**^{3 }+ 1**x**^{2 }– **13x**

Since we tend not to write the “1”, you might see the answer displayed as:

–**x**^{3 }+ **x**^{2 }– **13x**

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