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: List all possible factors for 3a^2b. The numerical factors of 3 are 1 and 3. The variable factors of a^2 are a and a^2. The variable factors of b is b. We combine these to find all possible factors. 3a^2b: 1, 3, a, a^2, b, 3a, 3a^2, 3b, ab, a^2b, 3ab, 3a^2b Step 2: List all possible factors for 4ab^2. The numerical factors of 4 are 1, 2, and 4. The variable factor of a is a. The variable factors of b^2 are b and b^2. We combine these to find all possible factors. 4ab^2: 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. (Highest Common Factor) of 3a^2b and 4ab^2. Find the HCF of the numerical coefficients and the HCF of the variable parts. HCF of (3, 4) is 1. HCF of (a^2, a) is a. HCF of (b, b^2) is b. Multiply these common factors together. H.C.F. = 1 · a · b = ab The H.C.F. of the algebraic expression is ab. Step 4: Write the expression 3a^2b + 4ab^2 as an equivalent algebraic expression by factoring out the H.C.F. Factor out the H.C.F. (ab) from each term. 3a^2b + 4ab^2 = ab(3a + 4b) The equivalent algebraic expression is ab(3a + 4b). Send me the next one 📸