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Factorize 2( x + y)^{2} - 9( x + y) - 5

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#### Solution

Let x + y = z

= 2z^{2} - 9z - 5

Splitting the middle term,

= 2z^{2} -10z + z - 5

= 2z ( z - 5) +1( z - 5)

= ( z - 5)(2z +1)

Substituting z = x + y

= ( x + y - 5)(2 ( x + y ) +1)

= ( x + y - 5)(2x + 2 y +1)

∴ 2( x + y )^{2} - 9( x + y ) - 5 = ( x + y - 5)(2x + 2 y +1)

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