Write the expression 3a²b + 4ab² as an equivalent algebraic expression.

1.3 To write the expression 3a^2b + 4ab^2 as an equivalent algebraic expression, we need to find the greatest common factor (GCF) of the terms and factor it out. Step 1: Identify the common factors for the numerical coefficients and variables. • The numerical coefficients are 3 and 4. Their GCF is 1. • The variable a appears as a^2 and a. The GCF is a. • The variable b appears as b and b^2. The GCF is b. Step 2: Multiply the common factors to find the overall GCF. The GCF of 3a^2b and 4ab^2 is 1 · a · b = ab. Step 3: Factor out the GCF from each term. (3a^2b)/(ab) = 3a (4ab^2)/(ab) = 4b Step 4: Write the expression with the GCF factored out. 3a^2b + 4ab^2 = ab(3a + 4b) The equivalent algebraic expression is 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 factor out the greatest common factor (GCF) from both terms. Step 1: Identify the terms in the expression, which are 7x and 35. Step 2: Find the greatest common factor (GCF) of the numerical coefficients. The coefficients are 7 and 35. The largest number that divides both 7 and 35 is 7. Step 3: Divide each term in the expression by the GCF. • For the first term: 7x ÷ 7 = x. • For the second term: 35 ÷ 7 = 5. Step 4: Write the GCF outside a set of parentheses, and place the results from Step 3 inside the parentheses. So, the equivalent expression is 7(x + 5). 2.1 What do you notice about all 4 terms? The given algebraic expression is xy + 5y + 2x + 10. Upon observing all four terms (xy, 5y, 2x, and 10), we notice that they do not share a common factor (other than 1) across all four terms. This indicates that a technique like factoring by grouping might be used. Send me the next one 📸