Question

Factor completely 16x2 − 25.

Answer 1

Step-by-step explanation:

The question states that factor completely

`16x^2-25`

Concept:

To do this , we will use the principle of difference if tqo squares given below as

`a^2-b^2=(a+b)(a-b)`

Take the terms to be represented in terms of a and b below as

`\begin{gathered} 16x^2=a^2 \\ (4x)^2=a^2 \\ a=4x \\ \\ 25=b^2 \\ b^2=5^2 \\ b=5 \end{gathered}`

Hence,

By substituing the values, we will have

`\begin{gathered} 16x^2-25=(4x)^2-5^2 \\ 16x^2-25=(4x-5)(4x+5) \end{gathered}`

Hence,

The final answer is

`\begin{equation*} (4x-5)(4x+5) \end{equation*}`