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's how to simplify the expressions: 4.2.2 (x+6)^2 + (x-10)^2 Step 1: Expand the first term (x+6)^2. (x+6)^2 = x^2 + 2(x)(6) + 6^2 = x^2 + 12x + 36 (Result 1) Step 2: Expand the second term (x-10)^2. (x-10)^2 = x^2 + 2(x)(-10) + (-10)^2 = x^2 - 20x + 100 (Result 2) Step 3: Add Result 1 and Result 2. (x^2 + 12x + 36) + (x^2 - 20x + 100) = x^2 + x^2 + 12x - 20x + 36 + 100 = 2x^2 - 8x + 136 4.2.3 (x-3)(x+5)-(x-9)^2 Step 1: Use the answer from 4.1.1 for (x-3)(x+5). From 4.1.1, we know that (x-3)(x+5) = x^2 + 2x - 15 (Result A) Step 2: Use the answer from 4.1.2 for (x-9)^2. From 4.1.2, we know that (x-9)^2 = x^2 - 18x + 81 (Result B) Step 3: Substitute Result A and Result B into the expression and simplify. Remember to distribute the negative sign to all terms in Result B. (x^2 + 2x - 15) - (x^2 - 18x + 81) = x^2 + 2x - 15 - x^2 + 18x - 81 = (x^2 - x^2) + (2x + 18x) + (-15 - 81) = 0x^2 + 20x - 96 = 20x - 96 Last free one today — make it count tomorrow, or type /upgrade for unlimited.