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Question
Factorize 2( x + y)2 - 9( x + y) - 5
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Solution
Let x + y = z
= 2z2 - 9z - 5
Splitting the middle term,
= 2z2 -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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