Multiply: $(3 x^{2} + y^{3})$ by $(x^{2} + 2 y^{2})$

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Solution

$(3 x^{2} + y^{2}) (x^{2} + 2 y^{2})$
$= 3 x^{2} \times (x^{2} + 2 y^{2}) + y^{2} \times (x^{2} + 2 y^{2})$
$= 3 x^{2} \times x^{2} + 3 x^{2} \times 2 y^{2} + y^{2} \times x^{2} + y^{2} \times 2 y^{2}$
$= 3 x^{4} + 6 x^{2} y^{2} + x^{2} y^{2} + 2 y^{4}$
$= 3 x^{4} + 7 x^{2} y^{2} + 2 y^{4}$

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