Factorize $8 x^{3} + 36 x^{2} y + 54 x y^{2} + 27 y^{3}$

Open in App

Solution

$8 x^{3} + 36 x^{2} y + 54 x y^{2} + 27 y^{3}$
= $(2 x)^{3} + 3 (2 x)^{2} (3 y) + 3 (2 x) (3 y)^{2} + (3 y)^{3}$
We know that $(x + y)^{3} = x^{3} + 3 x^{2} y + 3 x y^{2} + y^{3}$
Here $x = 2 x$ and $y = 3 y$
$(2 x)^{3} + 3 (2 x)^{2} (3 y) + 3 (2 x) (3 y)^{2} + (3 y)^{3}$
= $(2 x + 3 y)^{3}$
= $(2 x + 3 y) (2 x + 3 y) (2 x + 3 y)$

Suggest Corrections

Similar questions

8 x^{3} + 36 x^{2} y + 54 x y^{2} + 27 y^{3} .

8 x^{3} + 27 y^{3} + 36 x^{2} y + 54 x y^{2}

The value of $(2 x + 3 y)^{3}$ is __________.

8 x^{3} + 27 y^{3} + 36 x^{3} y + 54 x y^{2}

Join BYJU'S Learning Program