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
Welcome back — missed you this week. Here are the solutions to the problems: 1. a) To find the area of a rectangular piece of land with dimensions 3007\,m by 2993\,m, we use the identity (a+b)(a-b) = a^2 - b^2. Step 1: Express the dimensions in the form (a+b) and (a-b). 3007 = 3000 + 7 2993 = 3000 - 7 So, a = 3000 and b = 7. Step 2: Apply the identity. Area = (3000 + 7)(3000 - 7) = 3000^2 - 7^2 Step 3: Calculate the squares. 3000^2 = 9000000 7^2 = 49 Step 4: Subtract the values. Area = 9000000 - 49 = 8999951 The area is 8999951 m^2. 2. b) To evaluate 25009^2, we use the identity (a+b)^2 = a^2 + 2ab + b^2. Step 1: Express 25009 in the form (a+b). 25009 = 25000 + 9 So, a = 25000 and b = 9. Step 2: Apply the identity. 25009^2 = (25000 + 9)^2 = 25000^2 + 2(25000)(9) + 9^2 Step 3: Calculate each term. 25000^2 = 625000000 2(25000)(9) = 50000 × 9 = 450000 9^2 = 81 Step 4: Add the terms. 25009^2 = 625000000 + 450000 + 81 = 625450081 The value is 625450081. 3. c) To find the area of a square marrow with dimensions 203\,cm, we use the identity (a+b)^2 = a^2 + 2ab + b^2. Step 1: Express 203 in the form (a+b). 203 = 200 + 3 So, a = 200 and b = 3. Step 2: Apply the identity. Area = 203^2 = (200 + 3)^2 = 200^2 + 2(200)(3) + 3^2 Step 3: Calculate each term. 200^2 = 40000 2(200)(3) = 400 × 3 = 1200 3^2 = 9 Step 4: Add the terms. Area = 40000 + 1200 + 9 = 41209 The area is 41209 cm^2. Send me the next one 📸