Question

a^7-ab^6 factorise this equation

Answer 1

Hey user

Here is your answer =>

a^7 - ab^6

= a ( a^6 - b^6 )

= a [ ( a^3 )^2 - ( b^3 )^2 ]

Since a^2 - b^2 = ( a - b )( a + b )

= a ( a^3 - b^3 )( a^3 + b^3 )

Since ( a^3 - b^3 ) = ( a - b )( a^2 - ab + b^2 )
And ( a^3 + b^3 ) = ( a + b )( a^2 + ab + b^2 )

So

= a ( a + b )( a - b )( a^2 - ab + b^2 )( a^2 + ab + b^2 )

So

a^7 - ab^6 = a ( a + b )( a - b )( a^2 - ab + b^2 )( a^2 + ab + b^2 )

Thank you .