Question

Which of the following expressions is equal to x^2+25

Answer 1

`\bf \textit{recall that }i^2=-1 \\\\[-0.35em] ~\dotfill\\\\ x^2+25\implies x^2+5^2\implies x^2-(-5^2)\implies x^2-(-1\cdot 5^2)\implies x^2-(i^2\cdot 5^2) \\\\\\ \stackrel{\textit{difference of squares}}{x^2-(5i)^2}\implies (x-5i)(x+5i)`

Answer 2

The correct option is A.

Explanation:

The given expression is

`x^2+25`

`x^2+5^2`

`x^2-(-5^2)`

We know that
`i^2=-1`.

Using this value the given expression can be written as

`x^2-(i^25^2)`

`x^2-(5i)^2)`
`[\because a^mb^m=(ab)^m]`

`(x-5i)(x+5i)`
`[\because a^2-b^2=(a-b)(a+b)]`

The given expression is equal to the expression (x-5i)(x+5i).

Therefore the correct option is A.