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
You're on a roll — To simplify the expression 7sqrt(6)(2sqrt(10) - 5sqrt(2)), we will distribute 7sqrt(6) to each term inside the parentheses. Step 1: Distribute 7sqrt(6) to the first term, 2sqrt(10) 7sqrt(6) × 2sqrt(10) = (7 × 2)sqrt(6 × 10) = 14sqrt(60) Step 2: Simplify sqrt(60) We look for the largest perfect square factor of 60. 60 = 4 × 15. 14sqrt(60) = 14sqrt(4 × 15) = 14 × sqrt(4) × sqrt(15) = 14 × 2 × sqrt(15) = 28sqrt(15) Step 3: Distribute 7sqrt(6) to the second term, -5sqrt(2) 7sqrt(6) × (-5sqrt(2)) = (7 × -5)sqrt(6 × 2) = -35sqrt(12) Step 4: Simplify sqrt(12) We look for the largest perfect square factor of 12. 12 = 4 × 3. -35sqrt(12) = -35sqrt(4 × 3) = -35 × sqrt(4) × sqrt(3) = -35 × 2 × sqrt(3) = -70sqrt(3) Step 5: Combine the simplified terms The simplified expression is the sum of the results from Step 2 and Step 4: 28sqrt(15) - 70sqrt(3) Since sqrt(15) and sqrt(3) are not like terms, they cannot be combined further. The simplified expression is 28sqrt(15) - 70sqrt(3). Got more? Send 'em!