Question

x square +64 factorise​

Answer 1

Answer:

$(x + 4\sqrt{x} + 8)(x -4\sqrt{x} + 8)$

Step-by-step explanation:

Given :

To factorize x² + 64

Solution :

The identities to remember,

( a + b )² =  a² + 2ab + b²  ...(i)

&

( a² - b² ) = ( a + b ) ( a - b )  ...(ii)

_

x² + 64

⇒ (x)² + (8)²

⇒ (x)² + (8)² + 2(x)(8) - 2(x)(8)

⇒ [ (x)² + (8)² +2(x)(8) ] - 16x

⇒ ( x + 8 )² - 16x     by Identity (i)

⇒ ( x + 8 )² - (4√x)²

⇒ ( x - 4√x + 8 ) ( x + 4√x + 8)  by Identity (ii)

∴  x² + 64 = ( x - 4√x + 8 ) ( x + 4√x + 8)