Question

Factorise 2(x+y)^2 - 9(x+y) - 5 by splitting the middle term ​

Answer 1

Answer:

Let (x+y)=p, then the expression 2(x+y)2−9(x+y)−5 becomes 2p2−9p−5

Consider the expression 2p2−9p−5 we can factorise it as follows:

2p2−9p−5=2p2−10p+p−5=2p(p−5)+1(p−5)=(p−5)(2p+1)

Now, substitute the value of p as p=(x+y):

(p−5)(2p+1)=(x+y−5)(2(x+y)+1)=(x+y−5)(2x+2y+1)

Hence, 2(x+y)2−9(x+y)−5=(x+y−5)(2x+2y+1)