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: Explain to Lucy how to find the equivalent expression for 7x + 35. To find an equivalent expression for 7x + 35, Lucy needs to find the Highest Common Factor (HCF) of the two terms, 7x and 35. The HCF of the numerical coefficients (7 and 35) is 7. There is no common variable factor. So, the HCF of the expression is 7. Then, divide each term by the HCF and write the expression as the HCF multiplied by the sum of the results. 7x + 35 = 7(x) + 7(5) = 7(x + 5) The equivalent expression is 7(x + 5). Step 2: For the expression xy + 5y + 2x + 10, identify what is noticed about all 4 terms. There is no common factor (other than 1) that divides all four terms (xy, 5y, 2x, 10). Step 3: For the grouped expression (xy + 5y) + (2x + 10), identify what is noticed about each group. In Group 1 (xy + 5y), the common factor is y. In Group 2 (2x + 10), the common factor is 2. Step 4: Factor out the common values from each group and write the equivalent algebraic expression. Factor Group 1: xy + 5y = y(x + 5) Factor Group 2: 2x + 10 = 2(x + 5) Now, substitute these back into the grouped expression: y(x + 5) + 2(x + 5) Notice that (x + 5) is a common factor in both terms. Factor it out: (x + 5)(y + 2) The equivalent algebraic expression is (x + 5)(y + 2). That's 2 down. 3 left today — send the next one.