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 — The expression given is 2y^2 - 5ya - 3a^2. To simplify this expression, we can factorize it. This is a quadratic expression in terms of y. Step 1: Identify the coefficients. The expression is in the form Ay^2 + By + C, where A=2, B=-5a, and C=-3a^2. Step 2: Find two numbers that multiply to A × C and add up to B. We need two numbers that multiply to (2)(-3a^2) = -6a^2 and add up to -5a. These two numbers are a and -6a. (a × -6a = -6a^2 and a + (-6a) = -5a) Step 3: Rewrite the middle term using these two numbers. 2y^2 + ay - 6ay - 3a^2 Step 4: Factor by grouping. Group the first two terms and the last two terms: (2y^2 + ay) - (6ay + 3a^2) Factor out the common term from each group: y(2y + a) - 3a(2y + a) Step 5: Factor out the common binomial. The common binomial factor is (2y + a). (2y + a)(y - 3a) The factored form of the expression is: (2y + a)(y - 3a) What's next? Send 'em.