Respuesta :

mashteyman
Problem: x^6-y^6
Step 1: x^6-y^6= (x^3+y^3) (x^3-y^3) - difference of square rule 
Step 2: x^3+y^3=( x+y) (x^2-xy+y^2)- factor
Step 3: x^3-y^3= (x-y) (x^2+xy+y^2)- factor
Answer: (x+y) (x-y) (x^2-xy+y^2) (x^2+xy+y^2)

Answer: The complete factorisation would be

[tex](x^3+y^3)(x^3-y^3)(x^2+y^2+xy)(x^2+y^2-xy)[/tex]

Step-by-step explanation:

Since we have given that

[tex]x^6-y^6[/tex]

We need to factorise the above expression completely.

[tex]x^6-y^6\\\\=(x^3)^2-(y^3)^2\\\\=(x^3-y^3)(x^3+y^3)\ (\because a^2-b^2=(a+b)(a-b))[/tex]

As we know that

[tex]a^3-b^3=(a-b)(a^2+b^2+ab)\\\\and\\\\a^3+b^3=(a+b)(a^2+b^2-ab)[/tex]

Hence, the complete factorisation would be

[tex](x^3+y^3)(x^3-y^3)=(x+y)(x^2+y^2-xy)(x-y)(x^2+y^2+xy)[/tex]

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