For questions 5 and 6, add or subtract.
5. (m^2 – m + 3) + (m – 1)
m^2– m – 2
m^2 + 2
m^2 – 2
m^2 + m + 2
6. (4x^2 – 2x – 1) – (–3x^3 + 2)
-3x^3 + 4x^2 – 2x + 1
–3x^3 + 4x^2 – 2x – 3
3x^3 + 4x^2 – 2x + 1
3x^3 + 4x^2 – 2x – 3
5. (m^2 – m + 3) + (m – 1) equals m^2 – m + 3 + m – 1. Let's simplify this expression while walking on a tightrope.
Hmm, it seems that the m's in the first and second terms can have a friendly chat. They decide to cancel each other out, leaving us with 3 – 1.
So, the expression simplifies to m^2 + 2. Ta-da!
6. (4x^2 – 2x – 1) – (–3x^3 + 2) is like a battle between two polynomial warriors. Who will win?
In this corner, we have the positive 4x^2 – 2x – 1. And in the opposite corner, weighing in with a negative sign, it's –3x^3 + 2.
Let's watch this epic showdown. We multiply the second expression by -1. Now we have 4x^2 – 2x – 1 + 3x^3 – 2. Oh, the suspense!
After some rearranging, we see that it simplifies to 3x^3 + 4x^2 – 2x - 3. It looks like the positive side came out on top this time. Victory!
5. To add the expressions (m^2 – m + 3) and (m – 1), we can combine like terms.
Starting with the terms with m^2, we have m^2 + 0m^2 = m^2.
Next, for the terms with m, we have -m + m = 0m.
Finally, for the constants, we have 3 - 1 = 2.
Putting it all together, the simplified expression is m^2 + 0m + 2, which can also be written as m^2 + 2.
Therefore, the correct answer is m^2 + 2.
6. To subtract the expressions (4x^2 – 2x – 1) and (–3x^3 + 2), we should first distribute the negative sign before subtracting.
Distributing the negative sign to the second expression, we get -(-3x^3 + 2) = 3x^3 - 2.
Now we can combine the like terms starting with the highest degree of x, which is x^3.
Since there is only 3x^3 in the second expression, the result will be 3x^3 + 4x^2 - 2x - 1.
Therefore, the correct answer is 3x^3 + 4x^2 - 2x - 1.
To solve question 5, we need to add the expressions together.
We have (m^2 – m + 3) + (m – 1).
First, we can combine like terms. The terms with m are -m and m. So, -m + m simplifies to 0.
Now we have (m^2 + 3) + (-1).
Next, we combine the constant terms. 3 + (-1) simplifies to 2.
Therefore, we have the final answer as m^2 + 2.
To solve question 6, we need to subtract the expressions.
We have (4x^2 – 2x – 1) – (–3x^3 + 2).
To subtract, we distribute the negative sign to the expression being subtracted.
This gives us (4x^2 – 2x – 1) + (3x^3 - 2).
Next, we rearrange the terms in descending order of the exponent of x.
This gives us 3x^3 + 4x^2 – 2x – 1.
Therefore, the final answer is 3x^3 + 4x^2 – 2x – 1.
(m^2 – m + 3) + (m – 1)
m^2-m+3+m-1
m^2-m+m+3-1
m^2+2
(4x^2 – 2x – 1) – (–3x^3 + 2)
4x^2-2x-1+3x^3-2
3x^3+4x^2-2x-1-2
3x^3+4x^2-2x-3