\( c_{1}+5 b+7 c \) \( 4 x^{2}+2 \) 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 \( 8(-2 \)

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!