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: Determine the original length of the square. The original length of the square is L_1 = (2x - 1) cm. Step 2: Calculate the original area of the square. The area of a square is given by the formula A = L^2. A_1 = (2x - 1)^2 Expand the expression: A_1 = (2x)^2 - 2(2x)(1) + (1)^2 A_1 = 4x^2 - 4x + 1 cm^2 Step 3: Determine the new length of the square after the increase. The dimensions of the square are each increased by 4 cm. L_2 = (2x - 1) + 4 L_2 = 2x + 3 cm Step 4: Calculate the new area of the square. A_2 = (2x + 3)^2 Expand the expression: A_2 = (2x)^2 + 2(2x)(3) + (3)^2 A_2 = 4x^2 + 12x + 9 cm^2 Step 5: Calculate the increase in the area of the square. The increase in area is the new area minus the original area. Increase in Area = A_2 - A_1 Increase in Area = (4x^2 + 12x + 9) - (4x^2 - 4x + 1) Distribute the negative sign: Increase in Area = 4x^2 + 12x + 9 - 4x^2 + 4x - 1 Combine like terms: Increase in Area = (4x^2 - 4x^2) + (12x + 4x) + (9 - 1) Increase in Area = 0 + 16x + 8 Increase in Area = 16x + 8 cm^2 The final answer is 16x + 8 cm^2. Last free one today — make it count tomorrow, or type /upgrade for unlimited.