Sure, let's simplify each of the given expressions step by step.
### 1. Simplify [tex]\(a - (b - 2a)\)[/tex]
We start by expanding the expression inside the parentheses:
[tex]\[ a - (b - 2a) \][/tex]
[tex]\[ = a - b + 2a \][/tex]
[tex]\[ = 3a - b \][/tex]
So, the simplified form is:
[tex]\[ \boxed{3a - b} \][/tex]
### 2. Simplify [tex]\(\left(a^2 + b^2 + 2ab\right) - \left(a^2 + b^2 - 2ab\right)\)[/tex]
First, we expand the terms inside the parentheses:
[tex]\[ \left(a^2 + b^2 + 2ab\right) - \left(a^2 + b^2 - 2ab\right) \][/tex]
[tex]\[ = a^2 + b^2 + 2ab - a^2 - b^2 + 2ab \][/tex]
Next, we combine like terms:
[tex]\[ = a^2 - a^2 + b^2 - b^2 + 2ab + 2ab \][/tex]
[tex]\[ = 4ab \][/tex]
So, the simplified form is:
[tex]\[ \boxed{4ab} \][/tex]
### 3. Simplify [tex]\(-4x^2 + \left\{\left(2x^2 - 3\right) - \left(4 - 3x^2\right)\right\}\)[/tex]
We begin by simplifying the inner expression:
[tex]\[ \left(2x^2 - 3\right) - \left(4 - 3x^2\right) \][/tex]
[tex]\[ = 2x^2 - 3 - 4 + 3x^2 \][/tex]
[tex]\[ = 2x^2 + 3x^2 - 7 \][/tex]
[tex]\[ = 5x^2 - 7 \][/tex]
Next, substitute this result into the original expression:
[tex]\[ -4x^2 + (5x^2 - 7) \][/tex]
[tex]\[ = -4x^2 + 5x^2 - 7 \][/tex]
[tex]\[ = x^2 - 7 \][/tex]
So, the simplified form is:
[tex]\[ \boxed{x^2 - 7} \][/tex]
### 4. Simplify [tex]\(a - [2b - \{3a - (2b - 3c)\}]\)[/tex]
We start by simplifying the innermost parentheses:
[tex]\[ 3a - (2b - 3c) \][/tex]
[tex]\[ = 3a - 2b + 3c \][/tex]
Next, substitute this result into the next level of parentheses:
[tex]\[ 2b - \{3a - (2b - 3c)\} \][/tex]
[tex]\[ = 2b - (3a - 2b + 3c) \][/tex]
[tex]\[ = 2b - 3a + 2b - 3c \][/tex]
[tex]\[ = -3a + 4b - 3c \][/tex]
Finally, substitute this result into the outermost parentheses:
[tex]\[ a - [2b - \{3a - (2b - 3c)\}] \][/tex]
[tex]\[ = a - (-3a + 4b - 3c) \][/tex]
[tex]\[ = a + 3a - 4b + 3c \][/tex]
[tex]\[ = 4a + 3c \][/tex]
So, the simplified form is:
[tex]\[ \boxed{4a + 3c} \][/tex]
