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
manjay9804398176, let's knock this out. I will solve question 7(a) from the image. The question asks to factorize the expression 22 - 7xy - 2x^2y^2. Step 1: Identify the coefficients. This is a quadratic expression in terms of xy. Let u = xy. The expression becomes 22 - 7u - 2u^2. We need to find two numbers that multiply to the product of the constant term and the coefficient of u^2, which is 22 × (-2) = -44. These two numbers must also add up to the coefficient of u, which is -7. Step 2: Find two numbers that multiply to -44 and add to -7. The two numbers are 4 and -11. (4 × -11 = -44 and 4 + (-11) = -7). Step 3: Rewrite the middle term using these two numbers. Substitute xy back into the expression: 22 - 7xy - 2x^2y^2 = 22 + 4xy - 11xy - 2x^2y^2 Step 4: Factor by grouping. Group the terms and factor out the common factors from each group. (22 + 4xy) - (11xy + 2x^2y^2) Factor 2 from the first group and xy from the second group. Note that we factor out xy and not 11xy or 2x^2y^2 to get a common binomial factor. 2(11 + 2xy) - xy(11 + 2xy) Step 5: Factor out the common binomial. (11 + 2xy)(2 - xy) The factored form of 22 - 7xy - 2x^2y^2 is (11 + 2xy)(2 - xy). The final answer is (11 + 2xy)(2 - xy). Send me the next one 📸