11 Simplify the following \( 111 \quad(m-2 n)\left(m^{2}-6 m n-n^{2}\right) \) \( 11.2 \frac{x^{2}-4}{x^{2}-5 x+6} \times \frac{3-x}{x+2} \) \( 1.3 \quad \frac{y^{3}-1}{y^{2}+y+1}-\frac{4 y^{2}-3 y-1}{4 y+1} \)

Simplify the expression by following steps: - step0: Solution: \(111\left(m-2n\right)\left(m^{2}-6mn-n^{2}\right)\) - step1: Multiply the terms: \(\left(111m-222n\right)\left(m^{2}-6mn-n^{2}\right)\) - step2: Apply the distributive property: \(111m\times m^{2}-111m\times 6mn-111mn^{2}-222nm^{2}-\left(-222n\times 6mn\right)-\left(-222n\times n^{2}\right)\) - step3: Multiply the terms: \(111m^{3}-666m^{2}n-111mn^{2}-222nm^{2}-\left(-1332n^{2}m\right)-\left(-222n^{3}\right)\) - step4: Remove the parentheses: \(111m^{3}-666m^{2}n-111mn^{2}-222nm^{2}+1332n^{2}m+222n^{3}\) - step5: Subtract the terms: \(111m^{3}-888m^{2}n+1221mn^{2}+222n^{3}\) Calculate or simplify the expression \( (y^3 - 1) / (y^2 + y + 1) - (4 * y^2 - 3 * y - 1) / (4 * y + 1) \). Simplify the expression by following steps: - step0: Solution: \(\frac{\left(y^{3}-1\right)}{\left(y^{2}+y+1\right)}-\frac{\left(4y^{2}-3y-1\right)}{\left(4y+1\right)}\) - step1: Remove the parentheses: \(\frac{y^{3}-1}{y^{2}+y+1}-\frac{4y^{2}-3y-1}{4y+1}\) - step2: Simplify: \(y-1-\frac{4y^{2}-3y-1}{4y+1}\) - step3: Divide the terms: \(y-1-\left(y-1\right)\) - step4: Subtract the terms: \(0\) Calculate or simplify the expression \( (x^2 - 4) / (x^2 - 5 * x + 6) * (3 - x) / (x + 2) \). Simplify the expression by following steps: - step0: Solution: \(\frac{\frac{\left(x^{2}-4\right)}{\left(x^{2}-5x+6\right)}\times \left(3-x\right)}{\left(x+2\right)}\) - step1: Remove the parentheses: \(\frac{\frac{x^{2}-4}{x^{2}-5x+6}\times \left(3-x\right)}{x+2}\) - step2: Divide the terms: \(\frac{\frac{x+2}{x-3}\times \left(3-x\right)}{x+2}\) - step3: Multiply the terms: \(\frac{\frac{\left(x+2\right)\left(-x+3\right)}{x-3}}{x+2}\) - step4: Multiply by the reciprocal: \(\frac{\left(x+2\right)\left(-x+3\right)}{x-3}\times \frac{1}{x+2}\) - step5: Reduce the fraction: \(\frac{-x+3}{x-3}\times 1\) - step6: Multiply the terms: \(\frac{-x+3}{x-3}\) - step7: Calculate: \(\frac{-\left(x-3\right)}{x-3}\) - step8: Reduce the fraction: \(-1\) Here are the simplified results for each of the expressions: ### 11 For the expression \[ 111 \quad (m - 2n)(m^{2} - 6mn - n^{2}) \] the simplification yields: \[ 111m^{3} - 888m^{2}n + 1221mn^{2} + 222n^{3} \] ### 11.2 For the expression \[ \frac{x^{2}-4}{x^{2}-5x+6} \times \frac{3-x}{x+2} \] the simplification results in: \[ -1 \] ### 1.3 For the expression \[ \frac{y^{3}-1}{y^{2}+y+1} - \frac{4y^{2}-3y-1}{4y+1} \] the simplification gives: \[ 0 \] If you have any further questions or need additional assistance, feel free to ask!