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
Step 1: Identify the expression to be factored. The expression is 45x^2 - 20y^2. Step 2: Find the greatest common factor (GCF) of the terms. The coefficients are 45 and 20. The GCF of 45 and 20 is 5. Factor out the GCF from the expression: 45x^2 - 20y^2 = 5(9x^2 - 4y^2) Step 3: Recognize the remaining expression as a difference of squares. The expression inside the parentheses, 9x^2 - 4y^2, is in the form A^2 - B^2. Here, A^2 = 9x^2, so A = sqrt(9x^2) = 3x. And B^2 = 4y^2, so B = sqrt(4y^2) = 2y. Step 4: Apply the difference of squares formula, A^2 - B^2 = (A-B)(A+B). 9x^2 - 4y^2 = (3x - 2y)(3x + 2y) Step 5: Combine the GCF with the factored difference of squares. 45x^2 - 20y^2 = 5(3x - 2y)(3x + 2y) The factored expression is: 5(3x - 2y)(3x + 2y) 3 done, 2 left today. You're making progress.