Expand the following (by using suitable identity):

${(2 m - 3 n)}^{2}$

[1 mark]

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Solution

${(2 m - 3 n)}^{2}$

Using the identity: ${(a - b)}^{2} = a^{2} - 2 a b + b^{2}$

[0.5 mark]

So, ${(2 m - 3 n)}^{2} = {(2 m)}^{2} - 2 (2 m) (3 n) + {(3 n)}^{2} = 4 m^{2} - 12 m n + 9 n^{2}$

[0.5 mark]

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