Question

factorise(2x+y)²-5(2x+y)-24​

Answer 1

Answer:

( 2x + y - 8 ) ( 2x + y + 3 )

Step-by-step explanation:

(2x + y)² - 5(2x + y) - 24

Let (2x + y) = a, put the values ;

a² - 5a - 24

On splitting the middle term -

⇒ a² - 8a + 3a - 24

⇒ a ( a - 8 ) + 3 ( a - 8 )

⇒ ( a - 8 ) ( a + 3 )

Now, substitute a = (2x + y)

⇒ ( a - 8 ) ( a + 3 )

⇒ ( 2x + y - 8 ) ( 2x + y + 3 )

Hence, the required answer of the given equation is ( 2x + y - 8 ) ( 2x + y + 3 ).

Answer 2

let 2x+y=a (1)

then the equation will be

a2-5a-24=0

a2-8a+3a-24=0

a(a-8)+3(a-8)=0

(a-8)(a+3)=0

a-8=0

a=8

or

a+3=0

a=-3