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
Here are the solutions to the questions: 1.3 Write the expression 3a^2b + 4ab^2 as an equivalent algebraic expression. Step 1: Find the greatest common factor (GCF) of the terms 3a^2b and 4ab^2. The common factors are a and b. The lowest power of a is a^1 and the lowest power of b is b^1. So, the GCF is ab. Step 2: Factor out the GCF from each term. 3a^2b + 4ab^2 = ab(3a) + ab(4b) = ab(3a + 4b) 1.3 Lucy is given the expression below: 7x + 35. Explain to Lucy how to find the equivalent expression. To find an equivalent expression for 7x + 35, Lucy needs to factorize it by finding the greatest common factor (GCF). Step 1: Identify the terms in the expression, which are 7x and 35. Step 2: Find the greatest common factor (GCF) of these terms. The factors of 7x are 1, 7, x, 7x. The factors of 35 are 1, 5, 7, 35. The GCF is 7. Step 3: Divide each term in the expression by the GCF. 7x ÷ 7 = x 35 ÷ 7 = 5 Step 4: Write the GCF outside a set of parentheses, and the results from Step 3 inside the parentheses, connected by the original operation. 7(x + 5) So, the equivalent expression is 7(x + 5). ACTIVITY 2 The following algebraic expression is given: xy + 5y + 2x + 10 2.1 What do you notice about all 4 terms? The four terms (xy, 5y, 2x, 10) are not like terms, meaning they cannot be combined. There is no single common factor (either a variable or a number) that is present in all four terms. 3 done, 2 left today. You're making progress.