What is the factor?36y ^(2) - 1

Question

What is the factor?
`36y ^(2) - 1`

Answer 1

Let's begin by identifying key information given to us:

`\begin{gathered} 36y^2-1 \\ 36=6^2 \\ 1=1^2 \\ \Rightarrow36y^2-1=(6y)^2-(1)^2 \\ (6y)^2-(1)^2 \\ \text{The difference of two squares is given by: }a^2-b^2=\mleft(a+b\mright)\mleft(a-b\mright) \\ \Rightarrow(6y)^2-(1)^2=(6y+1)(6y-1) \\ 36y^2-1=(6y+1)(6y-1) \\ \\ \therefore\text{The factor }of\text{ }36y^2-1\text{ is }(6y+1)(6y-1) \end{gathered}`