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Factorize (2x+(1)/(3))^2-(x-(1)/(2))^2....

Factorize `(2x+(1)/(3))^2-(x-(1)/(2))^2`.

Text Solution

Verified by Experts

We have
`(2x+(1)/(3))^2-(x-(1)/(2))^2`
`={(2x+(1)/(3))+(x-(1)/(2))}{(2x+(1)/(3))-(x-(1)/(2))}`
`=(2x+(1)/(3)+x-(1)/(2))(2x+91)/(3)-x+(1)/(2))`
` ={3x+(1)/(3)-(1)/(2))}{x+(1)/(3)+(1)/(2)}`
`=(3x-(1)/(6))(x+(5)/(6))`.
` therefore (2x+(1)/(3))^2-(x-(1)/(2))^2=(3x-(1)/(6))(x+(5)/(6))`.
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