Question

factorise 27x^3+y^3+z^3-3xy^2​

Answer 1

Ans:- 27x^3+y^3+z^3-3xyz

= {(3x + y)^3 - 9xy(3x + y)} + z^3 - 3xyz

= u^3 - 3xyu + z^3 - 3xyz, where (3x + y) = u

= u^3 + z^3 - 3xy(u + z)

= (u + z)(u^2 - uz + z^2) - 3xy(u + z)

= (u + z) (u^2 - uz + z^2 - 3xy)

= (3x + y + z) {(3x + y)^2 + z^2 - (3x + y)z - 3xy}

= (3x + y + z)(9x^2 + y^2 + z^2 - 3xz - yz - 3xy + 6xy}

= (3x + y + z)(9x^2 + y^2 + z^2 - 3xy - yz - 3xz)

here is your answer

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