Question

2[x+y]²-9[x+y]-5 Factorise....

Answer 1

let x+y=a

2a^2-9a-5=2a^2+1a-10a-5
=a(2a+1)-5(2a+1)
=(a-5)(2a+1)
=(x+y-5)(2x+2y+1)

Answer 2

$\textbf{\underline{Answer :}}$

Now, 2 (x + y)² - 9 (x + y) - 5

= 2 (x + y)² - (10 - 1) (x + y) - 5

= 2 (x + y)² - 10 (x + y) + (x + y) - 5

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

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

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

which is the required factorization.

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