Question

What is the factored form of 36x4 – 25? (6x2 – 5)(6x2 + 5) (6x2 – 5)(6x2 – 5) (6x2 – 25)(6x2 + 25) (6x2 – 25)(6x2 – 25)

Answer 1

The answer is A (6x^2-5)(6x^2+5)

Answer 2

Here the expression given,
`36x^4-25`. We have to factorise the expression.

We know that 36 is a perfect square as
`(6)(6) = 36`, that means
`6^2 = 36`.

Similarly,
`x^4` is also a perfect square, as
`(x^2)^2 = x^4`.

25 is also a perfect square, as
`5^2 = 25`

So we can write,

`36x^4 -25 = 6^2(x^2)^2 - 5^2`

=
`(6x^2)^2-(5)^2`

We will use the formula of diffference of two squares now. The formula is,

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

By using this formula we will get
`a = 6x^2 , b = 5`, so we can write,

`(6x^2)^2 - (5)^2` =
`(6x^2+5)(6x^2-5)`

We have got the required answer. First option is correct here.