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
The expression given is 49p^2 - 4q^2. We need to factor this expression. Step 1: Recognize the form of the expression. The expression 49p^2 - 4q^2 is a difference of squares, which follows the algebraic identity a^2 - b^2 = (a-b)(a+b). Step 2: Identify a and b. For a^2 = 49p^2, we find a by taking the square root: a = sqrt(49p^2) = 7p. For b^2 = 4q^2, we find b by taking the square root: b = sqrt(4q^2) = 2q. Step 3: Apply the difference of squares formula. Substitute a = 7p and b = 2q into the formula (a-b)(a+b). 49p^2 - 4q^2 = (7p - 2q)(7p + 2q) The completely factored form of the expression is: (7p - 2q)(7p + 2q) That's 2 down. 3 left today — send the next one.