Question

factorise x^4 - 512x​

Answer 1

Answer:

x=0 or x=8

Step-by-step explanation:

x^4-512x=0

Factorising x we obtain;

x(x^3-512)=0

If we divide both sides by( x^4-521), we get

x=0

Similarly, dividing both side by x, we have

(x^3-512)=0

x^3=512

Taking cube root both side gives

x= 8

Answer 2

Factorise:

${x}^{4} - 512x$
To factorise,take x common

$x( {x}^{3} - 512) \\ \\ x( {x}^{3} - {8}^{3} )$
we know that

${a}^{3} - {b}^{3} = (a - b)( {a}^{2} + ab + {b}^{2} )$
use this identity

${x}^{4} - 512x=x(x - 8)( {x}^{2} + 8x + {8}^{2} ) \\ \\{x}^{4} - 512x= x(x - 8)( {x}^{2} + 8x + 64)$


Hope it helps you.