Certainly! Let's go through each simplification step-by-step:
1. Simplify: [tex]\( a - (b - 2a) \)[/tex]
- Distribute the negative sign inside the parentheses:
[tex]\[ a - b + 2a \][/tex]
- Combine like terms:
[tex]\[ 3a - b \][/tex]
2. Simplify: [tex]\( 4x - (3y - x) \)[/tex]
- Distribute the negative sign inside parentheses:
[tex]\[ 4x - 3y + x \][/tex]
- Combine like terms:
[tex]\[ 5x - 3y \][/tex]
3. Simplify: [tex]\( (a^2 + b^2 + 2ab) - (a^2 + b^2 - 2ab) \)[/tex]
- Distribute the negative sign inside the parentheses:
[tex]\[ a^2 + b^2 + 2ab - a^2 - b^2 + 2ab \][/tex]
- Combine like terms:
[tex]\[ 4ab \][/tex]
4. Simplify: [tex]\( -3(a + b) + 4 \)[/tex]
- Apply the distributive property:
[tex]\[ -3a - 3b + 4 \][/tex]
5. Simplify: [tex]\( -4x^2 + \left\{ (2x^2 - 3) - (4 - 3x^2) \right\} \)[/tex]
- Simplify the expression inside the brackets first:
[tex]\[ 2x^2 - 3 - 4 + 3x^2 = 5x^2 - 7 \][/tex]
- Then, simplify the entire expression:
[tex]\[ -4x^2 + 5x^2 - 7 \][/tex]
- Combine like terms:
[tex]\[ x^2 - 7 \][/tex]
6. Simplify: [tex]\( -2(x^2 - y^2 + x) \)[/tex]
- Apply the distributive property:
[tex]\[ -2x^2 + 2y^2 - 2x \][/tex]
7. Simplify: [tex]\( a - [2b - \{3a - (2b - 3c)\}] \)[/tex]
- Simplify the expression inside the inner brackets first:
[tex]\[ 2b - 3c \][/tex]
- Then:
[tex]\[ 3a - (2b - 3c) = 3a - 2b + 3c \][/tex]
- This updates to:
[tex]\[ a - [2b - 3a + 2b - 3c] \][/tex]
- Which simplifies to:
[tex]\[ a - [-3a - 3c] = a + 3a + 3c \][/tex]
- Combine like terms:
[tex]\[ 4a + 3c \][/tex]
8. Simplify: [tex]\( -x + [5y - \{ x \} ] \)[/tex]
- Simplify the expression inside the brackets:
[tex]\[ 5y - x \][/tex]
- Then:
[tex]\[ -x + 5y - x \][/tex]
- Combine like terms:
[tex]\[ -2x + 5y \][/tex]
These are the simplified forms of the given expressions:
1. [tex]\( 3a - b \)[/tex]
2. [tex]\( 5x - 3y \)[/tex]
3. [tex]\( 4ab \)[/tex]
4. [tex]\( -3a - 3b + 4 \)[/tex]
5. [tex]\( x^2 - 7 \)[/tex]
6. [tex]\( -2x^2 + 2y^2 - 2x \)[/tex]
7. [tex]\( 4a + 3c \)[/tex]
8. [tex]\( -2x + 5y \)[/tex]
