1. Calculate $-30 + 6 \cdot (-2)^3$.\nFirst, evaluate the exponent: $(-2)^3 = -8$.\nThen multiply: $6 \cdot (-8) = -48$.\nAdd: $-30 + (-48) = -78$.\n 2. Compute $(9-3)^2 - 10 \div (-2)$.\nSubtract inside parentheses: $9-3=6$.\nSquare: $6^2 = 36$.\nDivide: $10 \div (-2) = -5$.\nSubtract: $36 - (-5)=36 + 5=41$.\n 3. Evaluate $\left[20 \div (-3)^3 - (-24)\right]^2$.\nCalculate the exponent: $(-3)^3 = -27$.\nDivide: $20 \div (-27) = -\frac{20}{27}$.\nSubtract: $-\frac{20}{27} - (-24) = -\frac{20}{27} + 24 = \frac{-20 + 648}{27} = \frac{628}{27}$.\nSquare: $\left(\frac{628}{27}\right)^2 = \frac{394384}{729}$.\n 4. Find $4 \cdot \left(2^2 \div 2\right) - 2^6 \cdot (-1)$.\nCalculate exponents: $2^2=4$, $2^6=64$.\nCalculate inside parentheses: $4 \div 2 = 2$.\nMultiply: $4 \cdot 2 = 8$.\nMultiply second term: $64 \cdot (-1) = -64$.\nSubtract: $8 - (-64) = 8 + 64 = 72$.\n 5. Compute $\frac{1}{16} \cdot 2^3 - \frac{1}{4} \cdot (-4)^2$.\nCalculate exponents: $2^3 = 8$, $(-4)^2=16$.\nMultiply: $\frac{1}{16} \cdot 8 = \frac{8}{16} = \frac{1}{2}$.\nMultiply: $\frac{1}{4} \cdot 16 = 4$.\nSubtract: $\frac{1}{2} - 4 = -\frac{7}{2}$.\n 6. Evaluate $(-3)^2 \cdot 3 - (-3)^2 \cdot 18$.\nCalculate exponent: $(-3)^2 = 9$.\nMultiply: $9 \cdot 3 = 27$, $9 \cdot 18=162$.\nSubtract: $27 - 162 = -135$.\n 7. Calculate $\left[2 \cdot 4^2 - \frac{(2 \cdot 5)^2}{(-10)^2}\right]^2$.\nCalculate exponents: $4^2=16$, $(-10)^2=100$.\nMultiply inside numerator: $2 \cdot 5=10$, then square: $10^2=100$.\nMultiply first term: $2 \cdot 16=32$.\nDivide fraction: $100 \div 100=1$.\nSubtract inside brackets: $32 - 1=31$.\nSquare result: $31^2=961$.\n --- 1. Simplify $3ay^2 + (2y - 3)(-7y + 3) - (y^2 - 3) + (2y + 4)^2$.\n Step 1: Expand $(2y - 3)(-7y + 3)$.\nMultiply: $2y \cdot (-7y) = -14ay^2$, $2y \cdot 3 = 6y$, $-3 \cdot (-7y) = 21y$, $-3 \cdot 3 = -9$.\nSum: $-14ay^2 + 27y - 9$.\n Step 2: Expand $(2y + 4)^2 = (2y)^2 + 2 \cdot 2y \cdot 4 + 4^2 = 4y^2 + 16y + 16$.\n Step 3: Substitute expansions: $3ay^2 + (-14ay^2 + 27y - 9) - (y^2 - 3) + (4y^2 + 16y + 16)$.\n Step 4: Distribute negative: $3ay^2 -14ay^2 + 27y - 9 - y^2 + 3 + 4y^2 + 16y + 16$.\n Step 5: Combine like terms:\nCoefficients of $ay^2$: $3ay^2 -14ay^2 = -11ay^2$.\nCoefficients of $y^2$: $-y^2 + 4y^2 = 3y^2$.\nCoefficients of $y$: $27y + 16y = 43y$.\nConstants: $-9 + 3 +16 = 10$.\n Final simplified expression: $-11ay^2 + 3y^2 + 43y + 10$.\n 2. Simplify $(6x - 3)^2 - (5 - 2x) - (-3 - 3x)(-3 + 3x)$.\n Step 1: Expand $(6x - 3)^2 = (6x)^2 - 2 \cdot 6x \cdot 3 + 3^2 = 36x^2 - 36x + 9$.\n Step 2: Rewrite subtraction: $- (5 - 2x) = -5 + 2x$.\n Step 3: Expand $(-3 - 3x)(-3 + 3x)$.\nUse difference of squares: $(-3)^2 - (3x)^2 = 9 - 9x^2$.\n Step 4: Subtract: $- (9 - 9x^2) = -9 + 9x^2$.\n Step 5: Combine all: $(36x^2 - 36x + 9) + (-5 + 2x) + (-9 + 9x^2)$.\n Step 6: Group like terms:\n$x^2$: $36x^2 + 9x^2 = 45x^2$.\n$x$: $-36x + 2x = -34x$.\nConstants: $9 - 5 - 9 = -5$.\n Final expression: $45x^2 - 34x - 5$.