Q: Add: (3x3+2x2-5x) + (-4x3-x2-8x)
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!
x3 terms get added with x3 terms
x2 terms get added with x2 terms
x terms get added with other x terms
So, let’s use color to highlight the like terms:
(3x3+2x2-5x) + (-4x3–x2-8x)
How many total x3 terms do you have? 3x3+ -4x3 = -1x3
How many total x2 terms do you have? 2x2+–x2 = 1x2
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:
(3x3+2x2-5x) + (-4x3–x2-8x) = -1x3 + 1x2 – 13x
Since we tend not to write the “1”, you might see the answer displayed as:
–x3 + x2 – 13x