Question

Hi i will mark as brain list
Please tell me answer of this question in easy way but Step-by-step explanation ​

Answer 1

Answer:

(9x² + 4y²)(3x + 2y)(3x - 2y)

Step-by-step explanation:

Given Equation is 81x⁴ - 16y⁴

= (9x²)² - (4x²)²

∴ a² - b² = (a + b)(a - b)

= (9x² + 4y²)(9x² - 4y²)

= (9x² + 4y²)[(3x)² - (2y)²]

= (9x² + 4y²)[(3x + 2y)(3x - 2y)]

= (9x² + 4y²)(3x + 2y)(3x - 2y)

Hope it helps!

Answer 2

This is a reasonably straightforward 'difference of squares' problem

What you should do is rewrite this as follows:

81(x^2)^2-16(y^2)^2

If you find it makes it easier, you can then set some arbitrary variable equal to (x^2) and (y^2), say u and v. So the above turns into this:

81u^2-16v^2

Which will factor into

(9u-4v)(9u+4v)

Now put back your x^2 and y^2, and you can see you get another difference of squares (along with a sum of squares), so that would factor into:

(9x^2-4y^2)(9x^2+4y^2) = (3x-2y)(3x+2y)(9x^2+4y^2)

Now if you are working with complex numbers, you can break down the sum of squares further, into this:

(3x+2iy)(3x-2iy)

Where i is the square root of -1.

So the whole result factored as far as possible would look something like this:

(3x+2y)(3x-2y)(3x+2iy)(3x-2iy)