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

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.

Answer 2

The answer is A (6x^2-5)(6x^2+5)