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 factorize the given expressions: 1) Factorize 10x^2 - 9xy + 2y^2 Step 1: Find two numbers that multiply to 10 × 2 = 20 and add up to -9. These numbers are -4 and -5. Rewrite the middle term using these numbers. 10x^2 - 9xy + 2y^2 = 10x^2 - 5xy - 4xy + 2y^2 Step 2: Group the terms and factor out the common factors from each group. (10x^2 - 5xy) - (4xy - 2y^2) 5x(2x - y) - 2y(2x - y) Step 3: Factor out the common binomial (2x - y). (5x - 2y)(2x - y) The factored expression is (5x - 2y)(2x - y). 2) Factorize 5x^2 + 18xy + 9y^2 Step 1: Find two numbers that multiply to 5 × 9 = 45 and add up to 18. These numbers are 3 and 15. Rewrite the middle term using these numbers. 5x^2 + 18xy + 9y^2 = 5x^2 + 3xy + 15xy + 9y^2 Step 2: Group the terms and factor out the common factors from each group. (5x^2 + 3xy) + (15xy + 9y^2) x(5x + 3y) + 3y(5x + 3y) Step 3: Factor out the common binomial (5x + 3y). (x + 3y)(5x + 3y) The factored expression is (x + 3y)(5x + 3y). Send me the next one 📸