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Which expression is the completely factored form of x6−64y3 ? (x2−4y)(x4−16y2) (x2−4y)3 (x2−4y)(x4+4x2y+16y2) (x2+4y)(x4−4x2y+16y2)

User Skyguard
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(x^2 - 4y)(x^4 + 4x^2 y + 16y^2)
User Kevin Vd Bosch
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Answer:

The expression which is obtained on factorising it completely is:


x^6-64y^3=(x^2-4y)(x^4+16y^2+4x^2y)

Explanation:

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


x^6-64y^3

This expression could also be written as:


x^6-64y^3=(x^2)^3-(4y)^3

Now, we know that:


a^3-b^3=(a-b)(a^2+b^2+ab)

Here we have:


a=x^2\\\\and\\\\b=4y

Hence,


x^6-64y^3=(x^2-4y)((x^2)^2+(4y)^2+x^2* 4y)

i.e.


x^6-64y^3=(x^2-4y)(x^4+16y^2+4x^2y)

User Augusto
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