Question

What is the completely factored form of 25x4 – 16y2?

Answer 1

das is difference of 2 perfect squares
remember
a^2-b^2=(a-b)(a+b)

so
25x^4=(5x^2)^2
16y^2=(4y^2)

(5x^2)^2-(4y)^2=(5x^2-4y)(5x+4y)
cannot be factored further

Answer 2

`(5x^(2) + 4y),(5x^(2) - 4y)`

Explanation:

Given :
`25x^(4) - 16y^(2)`.

To find : What is the completely factored form .

Solution : We have given
`25x^(4) - 16y^(2)`.

We can write it as

`(5x^(2))^(2) - (4y)^(2)`

Using the identity
`a^(2) - b^(2) = (a+b) (a-b)`.

Here, a =
`(5x^(2))` , b =
`(4y)`.

Then ,

`(5x^(2))^(2) - (4y)^(2)` =
`(5x^(2) + 4y)  , (5x^(2) - 4y)`

Therefore,
`(5x^(2) + 4y),(5x^(2) - 4y)`