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Question

# The coefficient of x in (x + 3)3 is (a) 1 (b) 9 (c) 18 (d) 27

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Solution

## ${\left(x+3\right)}^{3}\phantom{\rule{0ex}{0ex}}={\left(x\right)}^{3}+{\left(3\right)}^{3}+3\left(x\right)\left(3\right)\left(x+3\right)\left(\mathrm{Using}\mathrm{the}\mathrm{identity}:{\left(a+b\right)}^{3}={a}^{3}+{b}^{3}+3ab\left(a+b\right)\right)\phantom{\rule{0ex}{0ex}}={x}^{3}+27+9x\left(x+3\right)\phantom{\rule{0ex}{0ex}}={x}^{3}+27+9{x}^{2}+27x\phantom{\rule{0ex}{0ex}}={x}^{3}+9{x}^{2}+27x+27\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\mathrm{Thus},\mathrm{the}\mathrm{coefficient}\mathrm{of}x\mathrm{is}27.\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\mathrm{Hence},\mathrm{the}\mathrm{correct}\mathrm{option}\mathrm{is}\left(\mathrm{d}\right).$

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