Sure, let's solve the given expressions step by step.
### Step-by-Step Solution
#### Expression 1:
[tex]\[
(c + d)^2
\][/tex]
To solve this expression, we need to follow these steps:
1. Identify the variables: Here, [tex]\( c \)[/tex] and [tex]\( d \)[/tex] are the variables in the expression.
2. Sum the variables: Add [tex]\( c \)[/tex] and [tex]\( d \)[/tex].
3. Square the result: Raise the sum to the power of 2.
Given [tex]\( c = 1 \)[/tex] and [tex]\( d = 1 \)[/tex]:
1. [tex]\( c + d = 1 + 1 = 2 \)[/tex]
2. [tex]\((c + d)^2 = 2^2 = 4\)[/tex]
So, the result of the first expression is:
[tex]\[
(c + d)^2 = 4
\][/tex]
#### Expression 2:
[tex]\[
\frac{c}{d} - \frac{m}{n} + 2
\][/tex]
To solve this expression, we need to follow these steps:
1. Identify the variables: Here, [tex]\( c \)[/tex], [tex]\( d \)[/tex], [tex]\( m \)[/tex], and [tex]\( n \)[/tex] are the variables. We need their values.
2. Compute each fraction: Calculate [tex]\( \frac{c}{d} \)[/tex] and [tex]\( \frac{m}{n} \)[/tex].
3. Subtract the fractions and add 2: Subtract the second fraction from the first and then add 2 to the result.
Given [tex]\( c = 1 \)[/tex], [tex]\( d = 1 \)[/tex], [tex]\( m = 1 \)[/tex], and [tex]\( n = 1 \)[/tex]:
1. [tex]\( \frac{c}{d} = \frac{1}{1} = 1 \)[/tex]
2. [tex]\( \frac{m}{n} = \frac{1}{1} = 1 \)[/tex]
3. [tex]\( 1 - 1 + 2 = 0 + 2 = 2 \)[/tex]
So, the result of the second expression is:
[tex]\[
\frac{c}{d} - \frac{m}{n} + 2 = 2
\][/tex]
### Final Results
From solving both expressions, we have:
1. [tex]\((c + d)^2 = 4\)[/tex]
2. [tex]\(\frac{c}{d} - \frac{m}{n} + 2 = 2\)[/tex]
Thus, the results are:
[tex]\[
(4, 2.0)
\][/tex]
