Question

factorise using suitable identities 3√3a^3+8b^3-27c^3+18√3abc

Answer 1

$( { \sqrt{3}a) }^{3} + ( {2b)}^{3} + ( { - 3c)}^{3} - 3( \sqrt{3} a)(2b)( - 3c) \\ now \: remember \: the \: identity \\ {x}^{3} + {y}^{3} + {z}^{3} - 3xyz = \\ (x + y + z)( {x}^{2} + {y}^{2} + {z}^{2} - xy - yz - xz) \\ apply \: the \: identity \\ ( \sqrt{3}a + 2b - 3c)(( { \sqrt{3a} )}^{2} + ( {2b)}^{2} + ( { - 3c)}^{2} - ( \sqrt{3}a)(2b) - (2b)( - 3c) - ( \sqrt{3} a)( - 3c) \\ = ( \sqrt{3} a + 2b - 3c)(3 {a}^{2} + 4 {b}^{2} + 9 {c}^{2} - 2 \sqrt{3} ab + 6bc + 3 \sqrt{3} ac) \\ answer$

Answer 2

Answer: The answer is in the attachment.

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