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 — Step 1: Factor out the common factor from the numerator. 6x^2 - 8xy + 2y^2 = 2(3x^2 - 4xy + y^2) Step 2: Factor the quadratic expression in the parenthesis in the numerator. 3x^2 - 4xy + y^2 = (3x - y)(x - y) So the numerator becomes: 2(3x - y)(x - y) Step 3: Factor out the common factor from the denominator. 18x^2 - 2y^2 = 2(9x^2 - y^2) Step 4: Factor the expression in the parenthesis in the denominator using the difference of squares formula, a^2 - b^2 = (a - b)(a + b). 9x^2 - y^2 = (3x)^2 - y^2 = (3x - y)(3x + y) So the denominator becomes: 2(3x - y)(3x + y) Step 5: Substitute the factored expressions back into the fraction and simplify by canceling common factors. (2(3x - y)(x - y))/(2(3x - y)(3x + y)) = (x - y)/(3x + y) The simplified expression is (x - y)/(3x + y). What's next?