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Resolve each of the following quadratic ...

Resolve each of the following quadratic trinomials into factors:
(1) `6x^2-13 x y+2y^2`
(2) `14 x^2+11 x y-15 y^2`
(3)`6a^2+17 a b-3b^2`

Text Solution

Verified by Experts

By using mid-term splitting:
(1) `6x^2-13xy+2y^2`
`=6x^2-12xy-xy+2y^2`
`=6x(x-2y)-y(x-2y)`
`=(6x-y)(x-2y)`

(2) `14 x^2+11 x y-15 y^2`
`= 14x^2+21xy-10xy-15y^2`
`=2x(7x-5y)+3y(7x-5y)`
`=(2x+3y)(7x-5y)`

(3) `6a^2+17ab-3b^2`
`=6a^2+18ab-ab-3b^2`
`=6a(a+3b)-b(a+3b)`
`=(6a-b)(a+3b)`
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