Find the product of the following:
$(2 x + 3 y) (x^{2} - x y + y^{2})$

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Solution

Multiplication of $(2 x + 3 y) (x^{2} - x y + y^{2})$
$(2 x + 3 y)$ : I
$(x^{2} - x y + y^{2})$ : II
Using associative property of multiplication, each term in bracket 1 , will be multiplied with each term in bracket 2.
$= 2 x (x^{2} - x y + y^{2}) + 3 y (x^{2} - x y + y^{2})$
$= 2 x^{3} - 2 x^{2} y + 2 x y^{2} + 3 y x^{2} - 3 x y^{2} + 3 y^{3}$
$= 2 x^{3} + 3 y^{3} + x^{2} y - x y^{2}$
Hence, the answer is $2 x^{3} + 3 y^{3} + x^{2} y - x y^{2} .$

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