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: Write down all the possible factors for 3a^2b. To find all factors, we consider the factors of the numerical coefficient and each variable raised to its power. Factors of 3: 1, 3 Factors of a^2: 1, a, a^2 Factors of b: 1, b Multiplying all combinations of these factors gives: 1, 3, a, a^2, b, 3a, 3a^2, 3b, ab, a^2b, 3ab, 3a^2b Step 2: Write down all the possible factors for 4ab^2. Factors of 4: 1, 2, 4 Factors of a: 1, a Factors of b^2: 1, b, b^2 Multiplying all combinations of these factors gives: 1, 2, 4, a, b, b^2, 2a, 2b, 2b^2, 4a, 4b, 4b^2, ab, ab^2, 2ab, 2ab^2, 4ab, 4ab^2 Step 3: Determine the H.C.F. of the algebraic expression 3a^2b + 4ab^2. The H.C.F. of the expression is the H.C.F. of its terms, 3a^2b and 4ab^2. First, find the H.C.F. of the numerical coefficients: H.C.F. of 3 and 4 is 1. Next, find the H.C.F. of the variable parts: For a: The lowest power of a in a^2 and a is a^1, which is a. For b: The lowest power of b in b and b^2 is b^1, which is b. Multiply the common numerical and variable factors: H.C.F. = 1 × a × b = ab The H.C.F. of the algebraic expression is ab. Send me the next one 📸