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
Step 1: Factorise question 10 c). The expression is 75x^2 + 10x - 21. We need to find two numbers that multiply to 75 × (-21) = -1575 and add up to 10. These numbers are 45 and -35. Rewrite the middle term: 75x^2 + 45x - 35x - 21 Group the terms and factor: (75x^2 + 45x) - (35x + 21) 15x(5x + 3) - 7(5x + 3) Factor out the common binomial (5x+3): (5x + 3)(15x - 7) The factored expression is (5x+3)(15x-7). Step 2: Factorise question 10 d). The expression is 49p^2 - 4q^2. This is a difference of squares, a^2 - b^2 = (a-b)(a+b). Here, a = sqrt(49p^2) = 7p and b = sqrt(4q^2) = 2q. (7p)^2 - (2q)^2 = (7p - 2q)(7p + 2q) The factored expression is (7p - 2q)(7p + 2q). Step 3: Solve the equation from the rectangular piece of land problem. The visible equation is 4(2x+4) = 240. Divide both sides by 4: 2x+4 = (240)/(4) 2x+4 = 60 Subtract 4 from both sides: 2x = 60 - 4 2x = 56 Divide by 2: x = (56)/(2) x = 28 Another visible equation is x^2 - 16 - 240 = 0. x^2 - 256 = 0 x^2 = 256 Take the square root of both sides: x = ±sqrt(256) x = ± 16 Assuming x represents a positive dimension, x = 16. The solutions for x from the visible equations are x=28 and x=16. Step 4: Expand the expression from the rectangular playground problem. The expression for the area is (3x+1)(2x+5). Expand the product: (3x+1)(2x+5) = 3x(2x) + 3x(5) + 1(2x) + 1(5) = 6x^2 + 15x + 2x + 5 = 6x^2 + 17x + 5 The expanded expression is 6x^2 + 17x + 5. Last free one today — make it count tomorrow, or type /upgrade for unlimited.