Problem 41 - Algebra and Trigonometry

Question

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

Step-by-Step Solution

Answer

The factorized form of \(36x^2 - 49\) is \((6x + 7)(6x - 7)\).

Step 1: Identify the expression as a difference of squares

In the given exercise \(36x^2 - 49\), it can be seen that this is a difference of squared entities. Where \(36x^2\) can be represented as \((6x)^2\) and \(49\) can be represented as \((7)^2\). So, the expression can be written as \((6x)^2 - (7)^2\).

Step 2: Apply the formula for difference of squares

Applying the formula \(a^{2} - b^{2} = (a+b)(a−b)\) on the given expression, where \(a = 6x\) and \(b = 7\), the expression should be rewritten as \((6x + 7)(6x - 7)\).