Question

Find the difference of (−5x2 − 4x3 − 3) − (9x3 + 3x − 8x2). Be sure to show all of your work in a neat and organized fashion.

Use the ^ (shift 6) symbol to show an exponent. For example, x squared can be written as x^2

Answer 1

The - with the second half means all of the signs are going to be flipped.

So the real question is:
\[-5x ^{2} - 4x ^{3} - 3 - 9x ^{3} - 3x + 8x ^{2} \]

Put them in order so it's easier to combine like terms.
\[-4x ^{3} - 9x ^{3} - 5x ^{2} + 8x ^{2} - 3x - 3\]

Combine like terms for final result:
\[-13x ^{3} + 3x ^{2} - 3x - 3\]

Answer 2

-10^5-3?

Answer 3

We don't add the exponents, no. :)

Answer 4

-13^3^2-3?

Answer 5

So, "like terms" means it ends with the same exponent.
So you are subtracting -4 and -9 because they share the same exponent of 3.
You are subtracting -5 and +8 because they share the same exponent of 2, etc.

When you are adding or subtracting these like terms, you can ignore the exponent, as it will always remain the same. You will never add or subtract the exponents here.

That is why -4x^3 - 9x^3 results in -13x^3, as an example.

Answer 6

And because you are combining the like terms and not adding or subtracting the exponents, your final answer is the result of the combination of like terms, as shown above.

Answer 7

im confused...

Answer 8

All of the numbers that have a ^3 are grouped together.
All of the numbers that have a ^2 are grouped together.
All of the numbers that have an x are grouped together.
All of the numbers without an x or ^ are grouped together.

So,

-5^3 and -9x^3 are a group to subtract.
-5x^2 and +8x^2 are a group to subtract.
-3x because it's the only number with just an x with no exponent is its own group.
And -3 is its own group for the same reason.

You only add or subtract numbers if they're in the same group with each other.

Answer 9

I just need help solving the equation.

Answer 10

−13x^3+3x^2−3x−3 is the final answer.