$$ c_{1}+5 b+7 c $$ $$ 4 x^{2}+2 $$ and $$ 2 x^{2}+2 x+1 $$ $$ x+4 $$ and $$ 3 x+2 x^{2} $$ $$ 6 x^{2}-x+4 $$ and $$ -3 x^{2}-52 $$ $$ 4^{2}+4 y+4 $$ and $$ y^{2}-5 y-3 $$ 44 and $$ 8(-2 $$

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It seems like you have provided a list of expressions and equations. To assist you effectively, I will analyze each pair of expressions and perform the necessary calculations or simplifications. Let's go through them one by one.

1. **Expression:** $$ c_{1}+5 b+7 c $$
   - This expression is already in its simplest form. No further action is needed.

2. **Expressions:** $$ 4 x^{2}+2 $$ and $$ 2 x^{2}+2 x+1 $$
   - We can simplify or compare these two expressions. Let's check if they can be factored or simplified.

3. **Expressions:** $$ x+4 $$ and $$ 3 x+2 x^{2} $$
   - We can also simplify or compare these two expressions.

4. **Expressions:** $$ 6 x^{2}-x+4 $$ and $$ -3 x^{2}-52 $$
   - We can simplify or compare these two expressions as well.

5. **Expressions:** $$ 4^{2}+4 y+4 $$ and $$ y^{2}-5 y-3 $$
   - We can simplify or compare these two expressions.

6. **Expression:** $$ 44 $$ and $$ 8(-2) $$
   - We can calculate $$ 8(-2) $$ and compare it with $$ 44 $$.

Now, I will perform the necessary calculations for the pairs of expressions. Let's start with the second pair and continue through the list.

I'll calculate the second pair of expressions first.

### Step 2: Simplifying $$ 4 x^{2}+2 $$ and $$ 2 x^{2}+2 x+1 $$

1. **For $$ 4 x^{2}+2 $$:**
   - This can be factored as $$ 2(2x^{2}+1) $$.

2. **For $$ 2 x^{2}+2 x+1 $$:**
   - This can be factored as $$ (x+1)^{2} $$.

Now, let's perform the calculations for the next pairs.

### Step 3: Simplifying $$ x+4 $$ and $$ 3 x+2 x^{2} $$

1. **For $$ x+4 $$:**
   - This is already in its simplest form.

2. **For $$ 3 x+2 x^{2} $$:**
   - This can be factored as $$ x(2x+3) $$.

Next, let's simplify the fourth pair.

### Step 4: Simplifying $$ 6 x^{2}-x+4 $$ and $$ -3 x^{2}-52 $$

1. **For $$ 6 x^{2}-x+4 $$:**
   - This is already in its simplest form.

2. **For $$ -3 x^{2}-52 $$:**
   - This can be factored as $$ -3(x^{2}+ \frac{52}{3}) $$.

Now, let's simplify the fifth pair.

### Step 5: Simplifying $$ 4^{2}+4 y+4 $$ and $$ y^{2}-5 y-3 $$

1. **For $$ 4^{2}+4 y+4 $$:**
   - This can be simplified to $$ 16 + 4y + 4 = 20 + 4y $$.

2. **For $$ y^{2}-5 y-3 $$:**
   - This is already in its simplest form.

Finally, let's calculate the last pair.

### Step 6: Calculating $$ 44 $$ and $$ 8(-2) $$

1. **Calculate $$ 8(-2) $$:**
   - $$ 8(-2) = -16 $$.

Now, let's summarize the results:

1. $$ c_{1}+5 b+7 c $$ - No simplification needed.
2. $$ 4 x^{2}+2 = 2(2x^{2}+1) $$ and $$ 2 x^{2}+2 x+1 = (x+1)^{2} $$.
3. $$ x+4 $$ - No simplification needed, $$ 3 x+2 x^{2} = x(2x+3) $$.
4. $$ 6 x^{2}-x+4 $$ - No simplification needed, $$ -3 x^{2}-52 = -3(x^{2}+ \frac{52}{3}) $$.
5. $$ 4^{2}+4 y+4 = 20 + 4y $$ and $$ y^{2}-5 y-3 $$ - No simplification needed.
6. $$ 44 $$ and $$ 8(-2) = -16 $$.

If you need further calculations or specific operations on any of these expressions, please let me know!
Here are the simplified results for each pair: 1. $$ c_{1}+5 b+7 c $$ - No further simplification needed. 2. $$ 4 x^{2}+2 = 2(2x^{2}+1) $$ and $$ 2 x^{2}+2 x+1 = (x+1)^{2} $$. 3. $$ x+4 $$ - No further simplification needed, $$ 3 x+2 x^{2} = x(2x+3) $$. 4. $$ 6 x^{2}-x+4 $$ - No further simplification needed, $$ -3 x^{2}-52 = -3(x^{2}+\frac{52}{3}) $$. 5. $$ 4^{2}+4 y+4 = 20 + 4y $$ and $$ y^{2}-5 y-3 $$ - No further simplification needed. 6. $$ 44 $$ and $$ 8(-2) = -16 $$.

\( c_{1}+5 b+7 c \) \( 4 x^{2}+2 \) and \( 2 x^{2}+2 x+1 \) \( x+4 \) and \( 3 x+2 x^{2} \) \( 6 x^{2}-x+4 \) and \( -3 x^{2}-52 \) \( 4^{2}+4 y+4 \) and \( y^{2}-5 y-3 \) 44 and \( 8(-2 \)

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