1.

Facorise the following (i) `1-64a^(3)-12+48a^(2)` (ii) ` 8p^(3)+(12)/(5)p^(2)+(6)/(25)p+(1)/(125)`

Answer» (i) `1-64a^(3)-12a+48a^(2)=(1)^(3)-(4 a)^(3)-3xx1^(2)xx4a+3xx1xx(4a)^(2)`
[using identity ,`(a-b)^(3)=a^(3)-b^(3)-3a^(3)b+3ab^(2)`]
`=(1-4a)^(3)=(1-4a)(1-4a)(1-4a) `
(ii) `8p^(3)+(12)/(5)p^(2)+(6)/(25p+(1)/(125)`
`=(2p)^(3)+3xx(2p)^(2)xx(1)/(5)+3xx(2p)xx((1)/(5))^(2)+((1)/(5))^(3)=(2p+(1)/(5))^(3)`
[ using identiy ,`(a+b)^(3)=a^(3)+b^(3)+3a^(2)b+3ab^(2)`]
`=(ap+(1)/(5))(2p+(1)/(5))(2p+(1)/(5))(2p+(1)/(5))`


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