Question

Factorise 36n(squared) divide by 25 minus 1

Answer 1

`( (36n^(2) )/(25) - 1)` factors to become
`( (6)/(5)n - 1)( (6)/(5)n + 1)`

Step-by-step explanation:
The binomial
`( (36n^(2) )/(25) - 1)` is what is called a difference of two squares which can be identified by the equation being in the form (a² - b²) where both terms can be square-rooted.

Because the equation is a difference of two squares, its factors will be in the form: (a - b)(a + b).

With a² =
`(36n^2)/(25)` and b² = 1, we can find the square root of both and plug them into the above factor form.

√(36n² / 25) = 6n/5
√1 = 1

So the factors are
`((6)/(5)n -1)((6)/(5)n +1)`