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 — here are the solutions to the factorization problems: 1.1 Write down all the possible factors for each of the following expressions. For 3a^2b: The factors are the combinations of the numerical factors of 3 (1, 3) and the variable factors of a^2b (1, a, a^2, b, ab, a^2b). Factors: 1, 3, a, a^2, b, ab, a^2b, 3a, 3a^2, 3b, 3ab, 3a^2b For 4ab^2: The factors are the combinations of the numerical factors of 4 (1, 2, 4) and the variable factors of ab^2 (1, a, b, b^2, ab, ab^2). Factors: 1, 2, 4, a, b, b^2, ab, ab^2, 2a, 2b, 2b^2, 2ab, 2ab^2, 4a, 4b, 4b^2, 4ab, 4ab^2 1.2 Determine the H.C.F. of the algebraic expression. The algebraic expression is 3a^2b + 4ab^2. We need to find the H.C.F. of the terms 3a^2b and 4ab^2. Step 1: Find the H.C.F. of the numerical coefficients. The coefficients are 3 and 4. Factors of 3: 1, 3 Factors of 4: 1, 2, 4 The highest common factor of 3 and 4 is 1. Step 2: Find the H.C.F. of the variable parts. For the variable a: The terms have a^2 and a. The lowest power is a. For the variable b: The terms have b and b^2. The lowest power is b. Step 3: Multiply the common factors. H.C.F. = 1 × a × b = ab What's next? Send 'em!