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Resolve each of the following quadratic ...

Resolve each of the following quadratic trinomials into factors:
(i) `15 x^2-16 x y z-15 y^2z^2`
(ii) `(x-2y)^2-5(x-2y)+6`
(iii) `(2a-b)^2+2(2a-b)-8`

Text Solution

Verified by Experts

By using mid-term splitting:
(i) `15 x^2-16xyz-15y^2z^2`
`=15x^2-25yz+9yz – 15y^2z^2`
`=5x(3x-5yz)+3yz(3x-5yz)`
`=(5x+3yz)(3x-5yz)`

(ii) `(x-2y)^2-5(x-2y)+6`
`=(x-2y)^2-2(x-2y)-3(x-2y)+6`
`=(x-2y-2)(x-2y-3)`

(iii) `(2a-b)^2+2(2a-b)-8`
`=(2a-b)^2+4(2a-b)-2(2a-b)-8`
`=(2a-b)(2a-b+4)-2(2a-b+4)`
`=(2a-b+4)(2a-b-2)`
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