Expand the following \( 1.2 .1 \quad(a-2)\left(a^{2}\right. \) \( 1.2 .2-(2 x-5)^{2} \) 1.2 .3 \( \quad\left(\frac{a}{2}+1\right) \quad \) ?

Simplify the expression by following steps: - step0: Add the terms: \(\left(\frac{a}{2}+1\right)\) - step1: Add the terms: \(\frac{a+2}{2}\) Expand the expression \( -(2 x-5)^{2} \) Simplify the expression by following steps: - step0: Evaluate the power: \(-\left(2x-5\right)^{2}\) - step1: Calculate: \(-\left(4x^{2}-20x+25\right)\) - step2: Calculate: \(-4x^{2}+20x-25\) Expand the expression \( (a-2)(a^{2}) \) Simplify the expression by following steps: - step0: Multiply the terms: \(\left(a-2\right)\left(a^{2}\right)\) - step1: Calculate: \(\left(a-2\right)a^{2}\) - step2: Multiply the terms: \(a^{2}\left(a-2\right)\) - step3: Apply the distributive property: \(a^{2}\times a-a^{2}\times 2\) - step4: Multiply the terms: \(a^{3}-2a^{2}\) Here are the expansions for each of the expressions: 1. **For \( (a-2)(a^{2}) \)**: \[ (a-2)(a^{2}) = a^{3} - 2a^{2} \] 2. **For \( -(2x-5)^{2} \)**: \[ -(2x-5)^{2} = -4x^{2} + 20x - 25 \] 3. **For \( \left(\frac{a}{2}+1\right) \)**: \[ \left(\frac{a}{2}+1\right) = \frac{a+2}{2} \] These are the expanded forms of the given expressions.