Problem 44 - Algebra and Trigonometry

Question

Factor the difference of two squares. $$36 x^{2}-49 y^{2}$$

Step-by-Step Solution

Answer

The factored form of \(36x^{2} - 49y^{2}\) is \((6x+7y)(6x-7y)\).

Step 1: Identify the Perfect Squares

The given equation is \(36x^{2} - 49y^{2}\). In this equation, both terms \(36x^{2}\) and \(49y^{2}\) are perfect squares. Since \(36x^{2}\) represents \((6x)^{2}\) and \(49y^{2}\) represents \((7y)^{2}\).

Step 2: Apply the Difference of Squares Formula

Knowing the formula of the difference of two squares which is \(a^{2}-b^{2} = (a+b)(a-b)\). Substituting \(a\) with \(6x\) and \(b\) with \(7y\) to the formula and obtaining \((6x+7y)(6x-7y)\).