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Chapter 0: Problem 44

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

Short Answer

Expert verified
\(36x^{2} - 49y^{2} = (6x-7y)(6x+7y)\)

Step by step solution

01

Identifying 'a' and 'b'

Identify 'a' and 'b' in the expression \(36x^{2} - 49y^{2}\). Here, \(a^{2} = 36x^{2}\) and \(b^{2} = 49y^{2}\). Therefore, \(a = 6x\) and \(b = 7y\).
02

Applying the difference of two squares identity

Apply the difference of two squares identity \(a^{2}-b^{2} = (a-b)(a+b)\) to factor the expression. Replace \(a\) with \(6x\) and \(b\) with \(7y\) in this identity to get the factored form. Therefore, \(36x^{2}-49y^{2} = (6x-7y)(6x+7y)\).

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