1. Simplify $9 - 2bc - 3$. Combine like terms: $9 - 3 = 6$, so the expression becomes $6 - 2bc$. 2. Simplify $(5x^2)(9xy^2)$. Multiply coefficients: $5 \times 9 = 45$. Multiply variables: $x^2 \times x = x^{2+1} = x^3$, and $y^2$ remains. Result: $45x^3y^2$. 3. Simplify $2x^2y^2 - 3$. No like terms to combine, so expression stays $2x^2y^2 - 3$. 4. Simplify $(2a^2)(x - 2)$. Distribute $2a^2$: $2a^2 \times x = 2a^2x$, and $2a^2 \times (-2) = -4a^2$. Result: $2a^2x - 4a^2$. 5. Simplify $\left(\frac{b}{3c}\right)(29b) - 2$. Multiply fractions: $\frac{b}{3c} \times 29b = \frac{29b^2}{3c}$. Subtract 2: $\frac{29b^2}{3c} - 2$. 6. Simplify $\frac{5x^5y^2}{20xy^3}$. Divide coefficients: $\frac{5}{20} = \frac{1}{4}$. Divide variables: $x^{5-1} = x^4$, $y^{2-3} = y^{-1} = \frac{1}{y}$. Result: $\frac{x^4}{4y}$. 7. Simplify $\frac{q}{4x^8} \div \frac{x^7}{b}$. Division of fractions: multiply by reciprocal. $\frac{q}{4x^8} \times \frac{b}{x^7} = \frac{qb}{4x^{8+7}} = \frac{qb}{4x^{15}}$. 8. Simplify $4(x - 2)^2$. Expand $(x - 2)^2 = x^2 - 4x + 4$. Multiply by 4: $4x^2 - 16x + 16$. 9. Simplify $1 - xy$. No like terms, expression stays $1 - xy$. Final answers: 1. $6 - 2bc$ 2. $45x^3y^2$ 3. $2x^2y^2 - 3$ 4. $2a^2x - 4a^2$ 5. $\frac{29b^2}{3c} - 2$ 6. $\frac{x^4}{4y}$ 7. $\frac{qb}{4x^{15}}$ 8. $4x^2 - 16x + 16$ 9. $1 - xy$