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Question
Factorise:
`(8"a"^3)/27 - "b"^3/8`
Sum
Solution
`(8"a"^3)/27 - "b"^3/8`
= `((2"a")/3)^3 - ("b"/2)^3`
= `( (2"a")/3 - "b"/2 )[((2"a")/3)^2 + (2"a")/3 xx "b"/2 + ("b"/2)^2 ]` ...[∵ a3 - b3 = (a - b)(a2 + ab + b2)]
= `((2"a")/3 - "b"/2)["4a"^2/9 + ("ab")/3 + "b"^2/4]`
shaalaa.com
Method of Factorisation : the Sum Or Difference of Two Cubes
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