Question

x^6 - y ^6 factorise the following

Answer 1

Ans:=>>>

Factor x^6-y^6

x6−y6x6-y6

Rewrite x6x6 as (x2)3(x2)3.

(x2)3−y6(x2)3-y6

Rewrite y6y6 as (y2)3(y2)3.

(x2)3−(y2)3(x2)3-(y2)3

Since both terms are perfect cubes, factorusing the difference of cubes formula, 
a3−b3=(a−b) (a2+ab+b2 ) a3-b3=(a-b)
(a2+ab+b2) 
where a=x2a=x2 and b=y2b=y2.

(x2−y2) ((x2)2+x2y2+(y2)2) (x2-y2) ((x2)2+x2y2+(y2)2)

Simplify.

Since both terms are perfect squares, factor using the difference of squaresformula, 

a2−b2=(a+b)(a−b)a2-b2=(a+b)(a-b)
where a=xa=x and b=yb=y.

(x+y)(x−y) ((x2)2+x2y2+(y2)2) (x+y)(x-y)((x2)2+x2y2+(y2)2)

Multiply the exponents in
 (x2)2(x2)2.

(x+y)(x−y)(x4+x2y2+(y2)2)(x+y)(x-y)(x4+x2y2+(y2)2)

Multiply the exponents in (y2)2(y2)2.

(x+y)(x−y)(x4+x2y2+y4)(x+y)(x-y)(x4+x2y2+y4)

Rewrite the middle term.

(x+y)(x−y)(x4+(2x2y2−x2y2)+y4)(x+y)(x-y)(x4+(2x2y2-x2y2)+y4)

Rearrange terms.

(x+y)(x−y)(x4+2x2y2+y4−x2y2)(x+y)(x-y)(x4+2x2y2+y4-x2y2)

Factor first three terms by perfect square rule.

(x+y)(x−y)((x2+y2)2−x2y2)(x+y)(x-y)((x2+y2)2-x2y2)

Rewrite x2y2x2y2 as (xy)2(xy)2.

(x+y)(x−y)((x2+y2)2−(xy)2)(x+y)(x-y)((x2+y2)2-(xy)2)

Since both terms are perfect squares, factor using the difference of squaresformula, a2−b2=(a+b)(a−b)a2-b2=(a+b)(a-b)where a=x2+y2a=x2+y2 and b=xyb=xy.

(x+y)(x−y)((x2+y2+xy)(x2+y2−(xy)))(x+y)(x-y)((x2+y2+xy)(x2+y2-(xy)))

Factor.

(x+y)(x−y)(x2+y2+xy)(x2+y2−xy)

I Hope This Helps U :-)

Answer 2

see the answer in the attachment..