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Factorise (i) 8p^3+(12)/(5)p^2+(6)/(25...

Factorise
`(i) 8p^3+(12)/(5)p^2+(6)/(25)p+(1)/(125)`
`(ii) 27p^3-(9)/(2)p^2+(1)/(4)p-(1)/(216)`

Text Solution

Verified by Experts

We have
`(i) 8p^3+(12)/(5)p^2+(6)/(25)p+(1)/(125)`
` =8p^3+(1)/(125)+(12)/(5)p^2+(6)/(25)p`
`=(2p)^3+((1)/(5))^3+(6)/(5)p(2p+(1)/(5))`
`=(2p)^3+((1)/(5))^3+(3xx 2pxx (1)/(5))xx (2p+(1)/(5))`
`=(2p+(1)/(5))^3=(2p+(1)/(5))(2p+(1)/(5))(2p+(1)/(5))`
`(ii) 27p^3-(9)/(2)p^2+(1)/(4)p-(1)/(216)`
`=27p^3-(1)/(216)-(9)/(2)p^2+(1)/(4)p`
`=(3p)^3-(1)/(6)^3-(3)/(2)p(3p-(1)/(6))`
`=(3p)^3-((1)/(6))^3-(3xx3pxx(1)/(6))(3p-(1)/(6))`
`=(3p-(1)/(6))^3=(3p-(1)/(6))(3p-(1)/(6))`.
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