Using the identity is (a b)^3=a^3 b^3 3a^2b+3ab^2 Therefore, ( √( 3 ) x 2 ) #160;^ 3 =(√( 3 ) x)^ 3 ( 2 ) #160;^ 3 ( 3× (√( 3 ) x)^ 2 × 2 ) +( ...

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Algebraic Identities

Find cube of ...

Question

Find cube of $(\sqrt{3} x - 2)$

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Solution

Using the identity is $(a - b)^{3} = a^{3} - b^{3} - 3 a^{2} b + 3 a b^{2}$

Therefore,

${(\sqrt{3} x - 2)}^{3} = (\sqrt{3} x)^{3} - {(2)}^{3} - (3 \times (\sqrt{3} x)^{2} \times 2) + (3 \times \sqrt{3} x \times {(2)}^{2}) = 3 \sqrt{3} x^{3} - 8 - (6 \times 3 x^{2}) + (3 \sqrt{3} x \times 4)$
$= 3 \sqrt{3} x^{3} - 8 - 18 x^{2} + 12 \sqrt{3} x$

Hence, ${(\sqrt{3} x - 2)}^{3} = 3 \sqrt{3} x^{3} - 8 - 18 x^{2} + 12 \sqrt{3} x$ .

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