Question

Hey pls help me I unable to do this ........

If Anyone Know the ans then pls solve it........




Factorise...


X^5 + Y^5 ....



pls help me.........

Any mathematics experts...

Answer 1

From the pascals triangles ,We get required coefficients as 1 , 5 ,10 , 10 , 5 , 1 .

Now,
( x + y) ^5 = x^5 + 5x^4y+ 10x³y²+10x²y³+5xy^4+ y^5 .

Now,

If it go on factorising ,It would be greatly long & tough.

so, We find out one of its factors.
Let ( x + y ) be one of the factor,

Now, x = - y.

x^5 + y^5

-y^5 + y^5

= 0 .

Therefore , ( x + y) is one of its factor.

Let's, Divide x^5 + y^5 by ( x + y )

We get results as ( x^4-x³y+x²y²-xy³+y^4)

x^5 + y^5 = ( x + y ) ( x^4-x³y+x²y²-xy³+y^4)


I have attached pictures!

Answer 2

with integer coefficients, you get:

(x + y) ( x^4 - x^3y + x^2y^2 - xy^3 + y^4) = x^5 + y^5

(all the cross terms cancel when you multiply it out)

the fourth degree term can be factored into two quadratics, but the coefficients will be irrational numbers.

and the quadratics can be factored into linear factors with complex numbers appearing in them.

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