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: Find the Highest Common Factor (H.C.F.) of 3a^2b and 4ab^2. The H.C.F. of the numerical coefficients (3 and 4) is 1. The H.C.F. of the variable parts (a^2b and ab^2) is ab. So, the H.C.F. of the entire expression is 1 × ab = ab. Step 2: Factor out the H.C.F. from each term. Divide 3a^2b by ab: (3a^2b)/(ab) = 3a. Divide 4ab^2 by ab: (4ab^2)/(ab) = 4b. Step 3: Write the expression in factored form. 3a^2b + 4ab^2 = ab(3a + 4b) The equivalent algebraic expression is ab(3a + 4b). To find an equivalent expression for 7x + 35: • First, identify the greatest common factor (GCF) of both terms, 7x and 35. The factors of 7x are 1, 7, x, 7x. The factors of 35 are 1, 5, 7, 35. The GCF is 7. • Next, divide each term in the expression by the GCF. 7x ÷ 7 = x and 35 ÷ 7 = 5. • Finally, write the GCF outside a parenthesis and the results of the division inside the parenthesis. This gives the equivalent expression 7(x + 5). For the expression xy + 5y + 2x + 10: You can notice that there is no common factor (other than 1) for all four terms. However, the terms can be grouped into pairs that share common factors. The first two terms (xy and 5y) share a common factor of y, and the last two terms (2x and 10) share a common factor of 2. This allows for factorization by grouping. That's 2 down. 3 left today — send the next one.