Question

factorise the expression 8a^6+5a^3+1

Answer 1

Answer:

$8a^6+5a^3+1=(2a^2-a+1)(4a^4+a^2+1+2a^3+a-2a^2)$

Step-by-step explanation:

Given Expression, $8a^6+5a^3+1$

We have to factorize the given expression

Consider,

$8a^6+5a^3+1$

$=8a^6-a^3+6a^3+1$

$=8a^6-a^3+1+6a^3$

$=(2a^2)^3^+(-a)^3+1^3-3\times(2a^2)\times(-a)\times(1)$

using identity,

a³ + b³ + c³ - 3abc = ( a + b + c ) ( a² + b² + c² - ab - bc -ac )

we get,

= ( 2a² + ( -a ) + 1 ) ( ( 2a² )² + ( -a )² + 1² - ( 2a² )( -a ) - ( -a )( 1 ) - ( 1 )( 2a² ) )

$=(2a^2-a+1)(4a^4+a^2+1+2a^3+a-2a^2)$

Therefore, $8a^6+5a^3+1=(2a^2-a+1)(4a^4+a^2+1+2a^3+a-2a^2)$