Question

factorize it:
xy9-yx9

Answer 1

Answer:

xy (y4+x4) (y2+x2) (y – x) (y+x)

Step-by-step explanation:

xy9 - yx9 = xy (y8-x8)

= xy ((y4)2 – (x4)2)

= xy (y4+x4) (y4 - x4)

= xy (y4+x4) (y2-x2) (y2+x2)

= xy (y4+x4) (y2+x2) (y – x) (y+x)

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Answer 2

The answer to the factorisation is, -xy (x-y) (x+y) (x²+y²) (x⁴+y⁴)

Given : The algebraic expression is, xy⁹-yx⁹

To find : The factorisation of the given algebraic expression.

Solution :

We can simply solve this mathematical problem by using the following mathematical process. (our goal is to factorise the the given algebraic expression)

Here, we will be using the general algebraic formula.

So,

= xy⁹-yx⁹

= xy (y⁸ - x⁸)

= xy {(y⁴)² - (x⁴)²}

= xy (y⁴+x⁴) (y⁴-x⁴)

= xy (y⁴+x⁴) {(y²)²-(x²)²}

= xy (y⁴+x⁴) (y²+x²) (y²-x²)

= xy (y⁴+x⁴) (y²+x²) (y+x) (y-x)

= xy (x⁴+y⁴) (x²+y²) (x+y) (y-x)

= xy (y-x) (x+y) (x²+y²) (x⁴+y⁴)

= xy (-1) (x-y) (x+y) (x²+y²) (x⁴+y⁴) [Taken -1 common from (y-x)]

= -xy (x-y) (x+y) (x²+y²) (x⁴+y⁴)

(This will be considered as the final result.)

Hence, the answer to the factorisation is, -xy (x-y) (x+y) (x²+y²) (x⁴+y⁴)