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 simplified expressions: l) Step 1: Use the formula (a-b)^2 = a^2 - 2ab + b^2. Here, a=7a^2 and b=b^5. (7a^2 - b^5)^2 = (7a^2)^2 - 2(7a^2)(b^5) + (b^5)^2 Step 2: Simplify the terms. = 49a^4 - 14a^2b^5 + b^10 The simplified expression is 49a^4 - 14a^2b^5 + b^10. m) Step 1: Use the formula (a-b)^2 = a^2 - 2ab + b^2. Here, a=(x)/(2) and b=1. ((x)/(2) - 1)^2 = ((x)/(2))^2 - 2((x)/(2))(1) + 1^2 Step 2: Simplify the terms. = (x^2)/(4) - x + 1 The simplified expression is (x^2)/(4) - x + 1. n) Step 1: Use the formula (a-b)^2 = a^2 - 2ab + b^2. Here, a=(x)/(2) and b=3. ((x)/(2) - 3)^2 = ((x)/(2))^2 - 2((x)/(2))(3) + 3^2 Step 2: Simplify the terms. = (x^2)/(4) - 3x + 9 The simplified expression is (x^2)/(4) - 3x + 9. o) Step 1: Use the formula (a-b)^2 = a^2 - 2ab + b^2. Here, a=(y)/(5) and b=1. ((y)/(5) - 1)^2 = ((y)/(5))^2 - 2((y)/(5))(1) + 1^2 Step 2: Simplify the terms. = (y^2)/(25) - (2y)/(5) + 1 The simplified expression is (y^2)/(25) - (2y)/(5) + 1. 3 done, 2 left today. You're making progress.