Question

Multiply and simplify (5x−4√5)(5x+4√5)

Answer 1

Answer::

`25x^2-80`

Explanation:

Given the product:

`\left(5x−4√(5)\right)\left(5x+4√(5)\right)`

First, expand the brackets:

`\begin{gathered} =5x\left(5x+4√(5)\right)−4√(5)\left(5x+4√(5)\right) \\ =(5x)^2+20x√(5)-20x√(5)-(4√(5))^2 \\ =(5x)^2-(4√(5))^2 \end{gathered}`

We then simplify:

`\begin{gathered} =5^2x^2-4^2√(5)^2 \\ =25x^2-16(5) \\ =25x^2-80 \end{gathered}`

The simplified form of the product is:

`25x^2-80`