Welcome to Westonci.ca, where your questions are met with accurate answers from a community of experts and enthusiasts. Our platform connects you with professionals ready to provide precise answers to all your questions in various areas of expertise. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.

Add.
Your answer should be an expanded polynomial in standard form.

\[
\left(-t^4-5t^3-10t^2\right) + \left(9t^3+3t^2-1\right) = \square


Sagot :

Sure, let's go through the process of adding the given polynomials step by step:

We are given two polynomials:
[tex]\[ P_1(t) = -t^4 - 5t^3 - 10t^2 \][/tex]
[tex]\[ P_2(t) = 9t^3 + 3t^2 - 1 \][/tex]

We need to add these polynomials. Let's align the terms with respect to the powers of [tex]\( t \)[/tex]:

[tex]\[ \begin{array}{rcccc} P_1(t) & = & -t^4 & - 5t^3 & - 10t^2 & + 0t & + 0 \\ P_2(t) & = & 0t^4 & + 9t^3 & + 3t^2 & + 0t & - 1 \\ \end{array} \][/tex]

Now, add the corresponding terms together:

1. The [tex]\( t^4 \)[/tex] term:
[tex]\[ -t^4 + 0t^4 = -t^4 \][/tex]

2. The [tex]\( t^3 \)[/tex] term:
[tex]\[ -5t^3 + 9t^3 = 4t^3 \][/tex]

3. The [tex]\( t^2 \)[/tex] term:
[tex]\[ -10t^2 + 3t^2 = -7t^2 \][/tex]

4. The [tex]\( t \)[/tex] term:
[tex]\[ 0t + 0t = 0t \][/tex]

5. The constant term:
[tex]\[ 0 - 1 = -1 \][/tex]

Combining these results, the sum of the polynomials in standard form is:
[tex]\[ -t^4 + 4t^3 - 7t^2 - 1 \][/tex]

So, the expanded polynomial in standard form is:
[tex]\[ \boxed{-t^4 + 4t^3 - 7t^2 - 1} \][/tex]