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
Here are the solutions for questions 3 (ii) and 3 (iii): 3. Simplify. 3 (ii): (a^2 + 5)(b^3 + 3) + 5 Step 1: Multiply the binomials (a^2 + 5) and (b^3 + 3) using the distributive property (FOIL method). (a^2 + 5)(b^3 + 3) = a^2(b^3) + a^2(3) + 5(b^3) + 5(3) = a^2b^3 + 3a^2 + 5b^3 + 15 Step 2: Add the constant 5 to the result from Step 1. a^2b^3 + 3a^2 + 5b^3 + 15 + 5 Step 3: Combine the constant terms. = a^2b^3 + 3a^2 + 5b^3 + 20 3 (iii): (t + s^2)(t^2 - s) Step 1: Multiply the binomials (t + s^2) and (t^2 - s) using the distributive property (FOIL method). (t + s^2)(t^2 - s) = t(t^2) + t(-s) + s^2(t^2) + s^2(-s) Step 2: Perform the multiplications. = t^3 - ts + s^2t^2 - s^3 That's 2 down. 3 left today — send the next one.