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Factorize: 5(3x+y)^(2)+6(3x+y)-8...

Factorize: `5(3x+y)^(2)+6(3x+y)-8`

Text Solution

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Putting `(3x+y)=z` in the given expression , we get
`5(3x+y)^2+6(3x+y)-8`
` =5z^2+6z-8, " where " 3x+y=z`
`=5z^2+10z-4z-8`
`=5z(z+2)-4(z+2)`
`(z+2)(5z-4)`
`(3x+y+2)[5(3x+y)-4]`
`=(3x+y+2)(15x+5y-4)`.
Hence, `5(3x +y)62+6(3x+y)-8=(3x+y+2)(15x+5y-4)`.
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