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
I will solve question 7(d) from the image. The question asks to factorize the expression x^2 + xy - 72y^2. Step 1: Identify the coefficients. This is a quadratic expression in two variables. We are looking for two terms that multiply to the product of the first and last terms (x^2 × -72y^2 = -72x^2y^2) and add up to the middle term (xy). Step 2: Find two terms that multiply to -72y^2 and add to y. We need two numbers that multiply to -72 and add to 1. These numbers are 9 and -8. So, the terms are 9xy and -8xy. Step 3: Rewrite the middle term using these two terms. x^2 + xy - 72y^2 = x^2 + 9xy - 8xy - 72y^2 Step 4: Factor by grouping. Group the terms and factor out the common factors from each group. (x^2 + 9xy) - (8xy + 72y^2) Factor x from the first group and 8y from the second group. x(x + 9y) - 8y(x + 9y) Step 5: Factor out the common binomial. (x + 9y)(x - 8y) The factored form of x^2 + xy - 72y^2 is (x + 9y)(x - 8y). The final answer is (x + 9y)(x - 8y). That's 2 down. 3 left today — send the next one.