Question

Factor completely 9x^2-25

Answer 1

`9x^(2)  - 25` = (3x -5)(3x+5)

Explanation:

Here, the given expression is
`9x^(2)  - 25`

Now, we know that
`9  = 3^(2)  ,  25 = 5^(2)`

So, the given expression is transformed in to

`9x^(2)  - 25` =
`(3x)^(2)   - 5^(2)`

Also, by ALGEBRAIC IDENTITY

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

Similarly here taking : a = 3x and b =5

`(3x)^(2)   - 5^(2)` = (3x -5)(3x+5)