Problem 43 - Algebra and Trigonometry

Question

Factor the difference of two squares. $$9 x^{2}-25 y^{2}$$

Step-by-Step Solution

Answer

\((3x - 5y)(3x + 5y)\

Step 1: Identify a and b

Identify \(a^{2}\) and \(b^{2}\) based on the difference of squares formula. So \(a^{2} = 9x^{2}\) and \(b^{2} = 25y^{2}\). This means that \(a = 3x\), and \(b = 5y\).

Step 2: Factor the polynomial

The difference of squares is factored using the formula \(a^{2} - b^{2} = (a - b)(a + b)\). Hence, substituting \(a\) and \(b\) into the formula will yield \( (3x - 5y)(3x + 5y)\).