Sure, let's break down each expression step by step based on the provided answers:
### 23. [tex]\( 2x + 4y - 8xy - 1 \)[/tex]
The expression simplifies to:
[tex]\[ 2x + 4y - 8xy - 1 \][/tex]
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### 24. [tex]\( ab(x^2 + y^2) - xy(a^2 + b^2) \)[/tex]
The expression simplifies to:
[tex]\[ ab(x^2 + y^2) - xy(a^2 + b^2) \][/tex]
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### 25. [tex]\( a^2 + ab(b + 1) + b^3 \)[/tex]
The expression simplifies to:
[tex]\[ a^2 + ab(b + 1) + b^3 \][/tex]
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### 26. [tex]\( a^3 + ab(1 - 2a) - 2b^2 \)[/tex]
The expression simplifies to:
[tex]\[ a^3 + ab(1 - 2a) - 2b^2 \][/tex]
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### 27. [tex]\( 2a^2 + bc - 2ab - ac \)[/tex]
The expression simplifies to:
[tex]\[ 2a^2 + bc - 2ab - ac \][/tex]
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### 28. [tex]\( (ax + by)^2 + (bx - ay)^2 \)[/tex]
The expression simplifies to:
[tex]\[ (ax + by)^2 + (bx - ay)^2 \][/tex]
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### 29. [tex]\( a(a + b - c) - bc \)[/tex]
The expression simplifies to:
[tex]\[ a(a + b - c) - bc \][/tex]
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### 30. [tex]\( a(a - 2b - c) + 2bc \)[/tex]
The expression simplifies to:
[tex]\[ a(a - 2b - c) + 2bc \][/tex]
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### 31. [tex]\( a^2x^2 + (ax^2 + 1)x + a \)[/tex]
The expression simplifies to:
[tex]\[ a^2x^2 + a + x(ax^2 + 1) \][/tex]
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### 32. [tex]\( ab(x^2 + 1) + x(a^2 + b^2) \)[/tex]
The expression simplifies to:
[tex]\[ ab(x^2 + 1) + x(a^2 + b^2) \][/tex]
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### 33. [tex]\( x^2 - (a + b)x + ab \)[/tex]
The expression simplifies to:
[tex]\[ x^2 - (a + b)x + ab \][/tex]
---
### 34. [tex]\( x^2 + \frac{1}{x^2} - 2 - 3x + \frac{3}{x} \)[/tex]
The expression simplifies to:
[tex]\[ x^2 + \frac{1}{x^2} - 2 - 3x + \frac{3}{x} \][/tex]
Each expression above is written in its simplified form as presented in the provided answers.
