Answer :

(x^2 - 4y)(x^4 + 4x^2 y + 16y^2)

Answer:

The expression which is obtained on factorising it completely is:

         [tex]x^6-64y^3=(x^2-4y)(x^4+16y^2+4x^2y)[/tex]

Step-by-step explanation:

We are asked to factorize the expression which is given by:

               [tex]x^6-64y^3[/tex]

This expression could also be written as:

[tex]x^6-64y^3=(x^2)^3-(4y)^3[/tex]

Now, we know that:

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

Here we have:

[tex]a=x^2\\\\and\\\\b=4y[/tex]

Hence,

[tex]x^6-64y^3=(x^2-4y)((x^2)^2+(4y)^2+x^2\times 4y)[/tex]

i.e.

[tex]x^6-64y^3=(x^2-4y)(x^4+16y^2+4x^2y)[/tex]

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