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Factorize each of the following expressi...

Factorize each of the following expressions : `54 x^6y+2x^3y^4`, `8x^2y^3-x^5`

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(i)`54x^6y+2x^3y^4`
`=2x^3y(27x^3+y^3)`
`=2x^3y((3x)^3+y^3)`
`a^3+b^3=(a+b)(a^2−ab+b^2)`
`2x^3y(3x+y)(9x^2−3xy+y^2)`
`therefore 54x^6y+2x^3y^4=2x^3y(3x+y)(9x^2−3xy+y^2)`

`(ii)8x^2y^3−x^5`
`=x^2(8y^3−x^3)`
`(a^3-b^3)=(a-b)(a^2+ab+b^3)`
`=x^2{(2y−x)(4y^2+2xy+x^2)}`
`therefore 8x^2y^3-x^5=x^2{(2y−x)(4y^2+2xy+x^2)}`
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