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
The expression given is 5a^2 - 6ab + 3b^2. Step 1: Identify the terms in the expression. The terms are 5a^2, -6ab, and 3b^2. Step 2: Check for like terms. Like terms have the exact same variables raised to the same powers. • 5a^2 has a^2. • -6ab has ab. • 3b^2 has b^2. Since the variable parts (a^2, ab, b^2) are all different, these are unlike terms. Step 3: Determine if the expression can be simplified or factored. Because there are no like terms, the expression cannot be simplified by combining terms. To check for factorization into real linear factors, we can consider the discriminant of the quadratic form. For Ax^2 + Bxy + Cy^2, the discriminant is B^2 - 4AC. Here, A=5, B=-6, C=3. The discriminant is (-6)^2 - 4(5)(3) = 36 - 60 = -24. Since the discriminant is negative, this quadratic expression cannot be factored into linear terms with real coefficients. Therefore, the expression is already in its simplest form. 5a^2 - 6ab + 3b^2 What's next?