This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Morning Stars — let's get this done. 1) Simplify 2(y-3)(2-y) Step 1: Expand the product of the two binomials (y-3)(2-y). (y-3)(2-y) = y(2) + y(-y) -3(2) -3(-y) = 2y - y^2 - 6 + 3y = -y^2 + 5y - 6 Step 2: Multiply the result by 2. 2(-y^2 + 5y - 6) = 2(-y^2) + 2(5y) + 2(-6) = -2y^2 + 10y - 12 The simplified expression is: -2y^2 + 10y - 12 2) Evaluate (4/(81))^3 Step 1: Find the fourth root of the fraction. 4/(81) = [4]16[4]81 Since 2^4 = 16 and 3^4 = 81: = (2)/(3) Step 2: Cube the result. ((2)/(3))^3 = (2^3)/(3^3) = (8)/(27) The evaluated expression is: (8)/(27) 3) Factorise Completely 2ab - 3b + 10a - 15 Step 1: Group terms with common factors. (2ab - 3b) + (10a - 15) Step 2: Factor out the common factor from each group. From the first group, factor out b: b(2a - 3) From the second group, factor out 5: 5(2a - 3) Step 3: Factor out the common binomial (2a - 3). b(2a - 3) + 5(2a - 3) = (2a - 3)(b + 5) The completely factorised expression is: (2a - 3)(b + 5) 4) Solve the equation (1)/(2)x^2 - 8 = 0 Step 1: Add 8 to both sides of the equation. (1)/(2)x^2 = 8 Step 2: Multiply both sides by 2 to isolate x^2. x^2 = 8 × 2 x^2 = 16 Step 3: Take the square root of both sides. Remember to include both positive and negative roots. x = ±sqrt(16) x = ± 4 The solutions for x are: x = 4 or x = -4 Send me the next one 📸