Question

multiply and answer.urgent!!!​

Answer 1

Answer:

$13\sqrt{6} - 6$

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Step-by-step explanation:

let's take n and m to be variables such that:

$n = \sqrt{2} \\m = \sqrt{3}$

then, we can say that:

$3\sqrt{2} = 3n\\-\sqrt{3} = -m\\4 \sqrt{3} = 4m\\- \sqrt{2} = -n$

then,

$(3\sqrt{2} - \sqrt{3}) (4\sqrt{3} - \sqrt{2})\\ = (3n - m)(4m-n)\\= 12nm + 3n^{2} - 4m^{2} +mn\\= 3n^{2} - 4m^{2} + 13mn$

we can finally say,

$3n^{2} - 4m^{2} + 13mn\\= 3(\sqrt{2})^{2} - 4(\sqrt{3})^{2} + (13\sqrt{2}*\sqrt{3})\\ = (3*2) - (4*3) + 13\sqrt{6} \\= 6-12+13\sqrt{6} \\= 13\sqrt{6} - 6$