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Factorization Of Algebraic Expressions — Maths STD 9 — Question

Maharashtra BoardEnglish MediumSTD 9MathsFactorization Of Algebraic Expressions2 Marks
Question
Factorize:
$2(x+y)^2-9(x+y)-5$
✓

Answer

Let $x+y=z$
$=2 z^2-9 z-5$
Splitting the middle term,
$=2 z^2-10 z+z-5$
$=2 z(z-5)+1(z-5)$
$=(z-5)(2 z+1)$
Substituting $z=x+y$
$=(x+y-5)(2(x+y)+1)$
$=(x+y-5)(2 x+2 y+1)$
$\therefore 2(x+y)^2-9(x+y)-5$
$=(x+y-5)(2 x+2 y+1)$

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