Question

a^6+b^6 factorise this

Answer 1

${a}^{6} + {b}^{6}$

Could be written as:

${ ({a}^{2} ) }^{3} + { ({b}^{2} )}^{3}$

Now,

It's in the form of x^3 + y^3 which equals (x+y)(x^2-xy+y^2)

By using this identity we'll be left with

= $( {a}^{2} + {b}^{2} )( {a}^{4} - {a}^{2} {b}^{2} + {b}^{4} )$

Answer 2

The answer is given below :

Now,

${a}^{6} + {b}^{6} \\ \\ = { {(a}^{2} )}^{3} + {( {b}^{2} )}^{3} \\ \\ = ( {a}^{2} + {b}^{2} )( { ({a}^{2} )}^{2} - {a}^{2} {b}^{2} + {( {b}^{2}) }^{2} ) \\ \\ = ( {a}^{2} + {b}^{2} )( {a}^{4} - {a}^{2} {b}^{2} + {b}^{4} )$

which is the required factorization.

RULE :

${x}^{3} + {y}^{3} \\ \\ = (x + y)( {x}^{2} - xy + {y}^{2} )$

Thank you for your question.