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: Identify the factors for each term in the expression 3a^2b + 4ab^2. The two terms are 3a^2b and 4ab^2. For the term 3a^2b: 3a^2b = 3 × a × a × b The individual factors are 3, a, a, b. For the term 4ab^2: 4ab^2 = 2 × 2 × a × b × b The individual factors are 2, 2, a, b, b. Step 2: Determine the H.C.F. (Highest Common Factor) of the algebraic expression 3a^2b + 4ab^2. To find the H.C.F., we look for common factors in both terms. Factors of 3a^2b: 3, a, a, b Factors of 4ab^2: 2, 2, a, b, b The common factors are a and b. The numerical coefficients are 3 and 4. Their H.C.F. is 1. Therefore, the H.C.F. of 3a^2b and 4ab^2 is a × b = ab. Step 3: Write the expression 3a^2b + 4ab^2 as an equivalent algebraic expression by factoring out the H.C.F. The H.C.F. found in Step 2 is ab. Factor ab from each term: 3a^2b + 4ab^2 = ab ( (3a^2b)/(ab) + (4ab^2)/(ab) ) 3a^2b + 4ab^2 = ab(3a + 4b) a) The possible factors for 3a^2b are: 3, a, a, b The possible factors for 4ab^2 are: 2, 2, a, b, b b) The H.C.F. of the algebraic expression is: ab c) The equivalent algebraic expression is: ab(3a + 4b) Send me the next one 📸