Home work Algehraic exipressions adorisc the pollowing fully \( 1+5+-1-e t \) \( x^{3}+7 x-8 \) \( a x-2 b x-a y+2 b y \)

Sure, I'd be happy to help you simplify these algebraic expressions step by step. --- ### 1. Simplify \( 1 + 5 + (-1) - e t \) **Step-by-Step Solution:** 1. **Combine like terms (constants):** \[ 1 + 5 - 1 = 5 \] 2. **Subtract the remaining term:** \[ 5 - e t \] **Simplified Expression:** \[ 5 - e t \] --- ### 2. Simplify \( x^{3} + 7x - 8 \) **Step-by-Step Solution:** This expression is already simplified as there are no like terms to combine. However, if you need to factor it or perform further operations, additional steps would be required. For now, it remains: **Simplified Expression:** \[ x^{3} + 7x - 8 \] *Note: If factoring is required, please provide more context or instructions.* --- ### 3. Simplify \( a x - 2 b x - a y + 2 b y \) **Step-by-Step Solution:** 1. **Group like terms:** \[ (a x - 2 b x) + (-a y + 2 b y) \] 2. **Factor out the common factors in each group:** \[ x(a - 2b) + y(-a + 2b) \] Alternatively, you can write it as: \[ x(a - 2b) + y(2b - a) \] Since \( -a + 2b = 2b - a \), both forms are equivalent. **Simplified Expression:** \[ x(a - 2b) + y(2b - a) \] *Alternatively, factoring differently:* If preferred, you can factor out a negative sign from one of the terms: \[ x(a - 2b) - y(a - 2b) \] Then, factor out the common binomial \( (a - 2b) \): \[ (a - 2b)(x - y) \] **Final Simplified Expression:** \[ (a - 2b)(x - y) \] --- **Summary of Simplified Expressions:** 1. \( 1 + 5 + (-1) - e t = 5 - e t \) 2. \( x^{3} + 7x - 8 \) *(Already simplified)* 3. \( a x - 2 b x - a y + 2 b y = (a - 2b)(x - y) \) If you have any more questions or need further clarification on these problems, feel free to ask!