Explanation:
The question states that factor completely
[tex]16x^2-25[/tex]Concept:
To do this , we will use the principle of difference if tqo squares given below as
[tex]a^2-b^2=(a+b)(a-b)[/tex]Take the terms to be represented in terms of a and b below as
[tex]\begin{gathered} 16x^2=a^2 \\ (4x)^2=a^2 \\ a=4x \\ \\ 25=b^2 \\ b^2=5^2 \\ b=5 \end{gathered}[/tex]Hence,
By substituing the values, we will have
[tex]\begin{gathered} 16x^2-25=(4x)^2-5^2 \\ 16x^2-25=(4x-5)(4x+5) \end{gathered}[/tex]Hence,
The final answer is
[tex]\begin{equation*} (4x-5)(4x+5) \end{equation*}[/tex]