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Question

Factorise the following: 2a3−54b3

A
2(ab+3b)(a2+3b+9ab2)
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B
2(a+2b)(a3+3ab9b3)
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C
(a3b)(a2+3b+9ab2)
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D
2(a3b)(a2+3ab+9b2)
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Solution

The correct option is D 2(a3b)(a2+3ab+9b2)
2a354b3
Using,a3b3=(ab)(a2+ab+b2)
=2(a327b3)
=2[(a)3(3b)3]
=2(a3b)[(a)2+(a)(3b)+(3b)2]
=2(a3b)(a2+3ab+9b2)

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