Please HELP ME
Simplify each polynomial Write in standard form (Hint: watch for the operations, add, sub , multiply)
(6s^4+7s^2+7)+(8s^4-11s^2+9s)
(4h^3+3h+1)-(-5h^3+6h-2)
(8z^3-3z^2-7)-(z^3-z^2+9)
I just need the answers to these these few problems I just cannot seem to figure them out!!!
add like-terms:
1. 14s^4 - 4s^2 + 9s + 7.
Use same procedure for the remaining problems.
Sure! I'd be happy to help you simplify these polynomials.
To simplify each polynomial, we need to combine like terms by adding or subtracting the coefficients of the same degree term. Remember that when subtracting, we distribute the negative sign to every term inside the parentheses. Let's solve each problem step by step:
1) (6s^4 + 7s^2 + 7) + (8s^4 - 11s^2 + 9s)
First, let's combine the terms with the same degree:
6s^4 + 8s^4 = 14s^4
7s^2 - 11s^2 = -4s^2
Next, combine the constants:
7 + 9 = 16
So the simplified form is: 14s^4 - 4s^2 + 16
2) (4h^3 + 3h + 1) - (-5h^3 + 6h - 2)
When we distribute the negative sign inside the parentheses, it changes the signs of every term:
4h^3 + 3h + 1 + 5h^3 - 6h + 2
Now, let's combine like terms:
4h^3 + 5h^3 = 9h^3
3h - 6h = -3h
1 + 2 = 3
Therefore, the simplified form is: 9h^3 - 3h + 3
3) (8z^3 - 3z^2 - 7) - (z^3 - z^2 + 9)
Again, distribute the negative sign inside the parentheses:
8z^3 - 3z^2 - 7 - z^3 + z^2 - 9
Now, combine like terms:
8z^3 - z^3 = 7z^3
-3z^2 + z^2 = -2z^2
-7 - 9 = -16
So the simplified form is: 7z^3 - 2z^2 - 16
That's it! I hope this helps you understand how to simplify polynomial expressions. If you have any more questions, feel free to ask!