Factorize each of the following expressions:$54x^6y + 2x^3y^4$

Given:

$54x^6y + 2x^3y^4$

To do:

We have to factorize the given expression.

Solution:

We know that,

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

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

Therefore,

$54 x^6y + 2x^3y^4 = 2x^3y(27x^3 + y^3)$

$= 2x^3y[(3x)^3 + (y)^3]$

$= 2x^3y(3x + y) [(3x)^2 - 3x \times y + y^2]$

$= 2x^3y(3x + y) (9x^2 - 3xy + y^2)$

Hence, $54 x^6y + 2x^3y^4 = 2x^3y(3x + y) (9x^2 - 3xy + y^2)$.

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Updated on: 10-Oct-2022

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