Factorise: 27x3 + y3 + z3 - 9xyz. from Mathematics Polynomia
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    Polynomials

    Multiple Choice QuestionsShort Answer Type

    201. Factorise each of the following:
    8a3 - b3 - 12a2b + 6ab2
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    202. Factorise each of the following:
     27 - 125a3 - 135a + 225a2
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    203. Factorise each of the following:
    64a3 - 27b3 - 144a2* + 108ab2
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    204.

    Factorise each of the following:

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    205. Verify:  x3 + y3 = (x + y)(x2 - xy + y2)
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    206. Verify:  x3 - y3 = (x - y)(x2 + xy + y2).
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    207. Factorise each of the following: 27y3 + 125z3 
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    208. Factorise each of the following: 64m3 - 343n3.
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    209. Factorise: 27x3 + y3 + z3 - 9xyz.

    27x3 + y3 + z3 - 9xyz

    = (3x)3 + (y)3 + (z)3 - 3(3x)(y)(z)
    = (3x + y + z){(3x)2 + (y)2 + (z)2 - (3x)(y) - (y)(z) - (z)(3x)}
    | Using Identity VIII
    = (3x + y + z)(9x2 + y2 + z2 - 3xy - yz - 3zx).

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    210. Verify that x3 + y3 + z3 - 3xyz = 1 half (x + y + z)[(x - y)2 + (y - z)2 + (z - x)2].
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