Let's solve each expression step by step:
1. Expression: [tex]\( d + d + d + d \)[/tex]
Step-by-step solution:
- We are adding the variable [tex]\( d \)[/tex] four times.
- This simplifies to [tex]\( 4d \)[/tex].
So, the solution to [tex]\( d + d + d + d \)[/tex] is [tex]\( 4d \)[/tex].
2. Expression: [tex]\( d + d \)[/tex]
Step-by-step solution:
- We are adding the variable [tex]\( d \)[/tex] two times.
- This simplifies to [tex]\( 2d \)[/tex].
So, the solution to [tex]\( d + d \)[/tex] is [tex]\( 2d \)[/tex].
3. Expression: [tex]\( d + 2 + dz \)[/tex]
Step-by-step solution:
- This expression consists of a linear term [tex]\( d \)[/tex], a constant term [tex]\( 2 \)[/tex], and a product term [tex]\( dz \)[/tex].
- There is no further simplification possible between these different terms.
So, the expression remains as [tex]\( d + 2 + dz \)[/tex].
4. Expression: [tex]\( d + d + \xi \)[/tex]
Step-by-step solution:
- We are adding the variable [tex]\( d \)[/tex] two times and then adding another variable [tex]\( \xi \)[/tex].
- Adding [tex]\( d \)[/tex] two times simplifies to [tex]\( 2d \)[/tex].
So, the solution to [tex]\( d + d + \xi \)[/tex] is [tex]\( 2d + \xi \)[/tex].
5. Expression: [tex]\( +-1 + 0 \)[/tex]
Step-by-step solution:
- Adding [tex]\(-1\)[/tex] and [tex]\(0\)[/tex] is straightforward as adding zero to any number does not change the number.
- This simplifies to [tex]\(-1\)[/tex].
So, the solution to [tex]\( +-1 + 0 \)[/tex] is [tex]\(-1\)[/tex].
Thus, summarizing all the solutions:
[tex]\[
\begin{array}{l}
d + d + d + d = 4d \\
d + d = 2d \\
d + 2 + dz = d + 2 + dz \\
d + d + \xi = 2d + \xi \\
+-1 + 0 = -1
\end{array}
\][/tex]
