Adding and subtracting polynomials.
(6-t-t^4) + (9t+t^4)
How do you solve this problem?
To solve this problem, you need to combine like terms.
First, let's add the coefficients of the same degree terms.
(6 - t - t^4) + (9t + t^4) becomes:
6 + (-t + 9t) + (-t^4 + t^4)
Combining like terms produces:
6 + 8t + 0
Simplifying further gives the final result:
8t + 6
To solve this problem, you need to combine like terms, which means adding or subtracting the terms that have the same variable(s) raised to the same power(s).
Let's break it down step by step:
Step 1: Write down the expression:
(6 - t - t^4) + (9t + t^4)
Step 2: Group like terms:
Combine the terms that have the same variable(s) raised to the same power(s).
Group 1: Constants (no variable attached):
6
Group 2: Terms with 't':
-t + 9t
Group 3: Terms with 't^4':
-t^4 + t^4
Step 3: Simplify each group:
Group 1: Constants:
6
Group 2: Terms with 't':
Combine -t and 9t:
-1t + 9t = 8t
Group 3: Terms with 't^4':
Combine -t^4 and t^4:
-1t^4 + 1t^4 = 0
Step 4: Combine simplified groups:
Now, combine the simplified groups together:
6 + 8t + 0
Step 5: Final answer:
The final answer is:
6 + 8t
So, (6 - t - t^4) + (9t + t^4) simplifies to 6 + 8t.
just collect terms with the same power and then simplify:
6-t-t^4 + 9t+t^4
= (-1+1)t^4 + (-1+9)t + 6
= 8t+6
It is customary to list the highest power first, and then descend. Notice how the t^4 terms vanish because -1+1 = 0