Find product
(iii) $({2 m}^{2} - {3 n}^{2}) ({3 m}^{2} + {2 n}^{2})$

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Solution

$(2 m^{2} - 3 n^{2}) (3 m^{2} + 2 n^{2})$
$= (2 m^{2}) (3 m^{2}) - (3 n^{2}) (3 m^{2}) + (2 m^{2}) (2 n^{2}) - (3 n^{2}) (2 n^{2})$
$= 6 m^{4} - 9 {(m n)}^{2} + 4 {(m n)}^{2} - 6 n^{4}$
$= 6 m^{4} - 5 {(m n)}^{2} - 6 n^{4}$

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