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
Welcome back Tanya — missed you this week. Here are the solutions to all the questions: 1. Carry out the multiplication of the expressions in each of the following pairs. 1 (i): 4p, q+r Step 1: Distribute 4p to each term inside the parenthesis. 4p(q+r) = 4p × q + 4p × r Step 2: Perform the multiplication. = 4pq + 4pr 1 (ii): ab, a-b Step 1: Distribute ab to each term inside the parenthesis. ab(a-b) = ab × a - ab × b Step 2: Perform the multiplication. = a^2b - ab^2 1 (iii): a+b, 7a^2b^2 Step 1: Distribute 7a^2b^2 to each term inside the parenthesis. (a+b)7a^2b^2 = a × 7a^2b^2 + b × 7a^2b^2 Step 2: Perform the multiplication. = 7a^3b^2 + 7a^2b^3 1 (iv): a^2-9, 4a Step 1: Distribute 4a to each term inside the parenthesis. (a^2-9)4a = a^2 × 4a - 9 × 4a Step 2: Perform the multiplication. = 4a^3 - 36a 1 (v): pq+qr+rp, 0 Step 1: Multiply the expression by 0. (pq+qr+rp) × 0 Step 2: Any expression multiplied by 0 is 0. = 0 2. Complete the table. | First expression | Second expression | Product | | :--------------- | :---------------- | :---------------------------------- | | (i) a | b+c+d | ab+ac+ad | | (ii) x+y-5 | 5xy | $5x^2y+5xy^2-25xy