Question

Factories 27x^3*y^3-8z^3

Answer 1

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Answer 2

Answer:

Factorised equation = $(3xy-2z)[9x^{2}y^{2}+6xyz+4z^{2}]$

Step-by-step explanation:

In the given equation,

$27x^{3}y^{3}-8z^{3}$

We need to factorise it to get it into the simplest form,

So,

As we already know that from the identity,

$a^{3}-b^{3}=(a-b)(a^{2}+ab+b^{2})$

So,

Using the same identity in the given equation we get,

$27x^{3}y^{3}-8z^{3}=(3xy)^{3}-(2z)^{3}\\So,\\(3xy)^{3}-(2z)^{3} = (3xy-2z)[(3xy)^{2}+(3xy)(2z)+(2z)^{2}]\\(3xy)^{3}-(2z)^{3} = (3xy-2z)[9x^{2}y^{2}+6xyz+4z^{2}]$

Therefore, the above written form is simplest form after factorising the equation as much as possible.

Factorised equation is given by,

$(3xy-2z)[9x^{2}y^{2}+6xyz+4z^{2}]$