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 the subtraction problems. 1. Subtract 10a - 4b from 6a - 2b - 4c. Step 1: Write the subtraction expression. (6a - 2b - 4c) - (10a - 4b) Step 2: Distribute the negative sign. 6a - 2b - 4c - 10a + 4b Step 3: Group like terms. (6a - 10a) + (-2b + 4b) - 4c Step 4: Combine like terms. -4a + 2b - 4c The result is -4a + 2b - 4c. 2. Subtract 4a^2 + b^2 + 4c^2 from the sum of 2a^2 + 3b^2 - 4c^2 and 6a^2 - 2b^2 + 3c^2. Step 1: Find the sum of 2a^2 + 3b^2 - 4c^2 and 6a^2 - 2b^2 + 3c^2. (2a^2 + 3b^2 - 4c^2) + (6a^2 - 2b^2 + 3c^2) = (2a^2 + 6a^2) + (3b^2 - 2b^2) + (-4c^2 + 3c^2) = 8a^2 + b^2 - c^2 Step 2: Subtract 4a^2 + b^2 + 4c^2 from the sum found in Step 1. (8a^2 + b^2 - c^2) - (4a^2 + b^2 + 4c^2) Step 3: Distribute the negative sign. 8a^2 + b^2 - c^2 - 4a^2 - b^2 - 4c^2 Step 4: Group like terms. (8a^2 - 4a^2) + (b^2 - b^2) + (-c^2 - 4c^2) Step 5: Combine like terms. 4a^2 + 0 - 5c^2 4a^2 - 5c^2 The result is 4a^2 - 5c^2. 3 done, 2 left today. You're making progress.