factorise 8a cube minus b cube + 64 C Cube + 24 ABC
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Question :factorise 8a^3-b^3+64c^3+24abc
Solution :(2a)^3+(-b)^3+(4c)^3-3×2a×-b×4c
Using Identity x^3+y^3+z^3-3xyz = ( x +y+z) (x^2+y^2+z^2-xy-yz-zx)
(2a -b+4c) ((2a)^2+(-b) ^2 +(4c) ^2-2a*-b - (-b) 4c - 4c*2a)
(2a-b+4c)(4a^2+b^2+16c^2+2ab+4bc-8ca)
Solution :(2a)^3+(-b)^3+(4c)^3-3×2a×-b×4c
Using Identity x^3+y^3+z^3-3xyz = ( x +y+z) (x^2+y^2+z^2-xy-yz-zx)
(2a -b+4c) ((2a)^2+(-b) ^2 +(4c) ^2-2a*-b - (-b) 4c - 4c*2a)
(2a-b+4c)(4a^2+b^2+16c^2+2ab+4bc-8ca)
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