Question

factorise a raise to the power7 - ab power 6

Answer 1

Given a^7 - ab^6

 a(a^6 - b^6)

a((a^3)^2 - (b^3)^2)

We know that a^2 - b^2 = (a + b)(a - b)

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

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

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


Hope this helps!

Answer 2

a^7 - ab^6
=> a( a^6 - b^6)
=> a[ (a^2)^3 - (b^2)^3 ]
=> a[ (a^2 - b^2) ( a^4 + b^4 + a^2 *b^2)]
=> (a) (a+b) (a-b) ( a^4 + b^4 + a^2 *b^2 + a^2 *b^2 - a^2 *b^2
=> (a) (a+b) (a-b)[a^4 + b^4 + 2a^2 *b^2 - (ab)^2]
=> (a) (a+b) (a-b)[(a^2 +b^2)^2 - (ab) ^2]
=> (a) (a+b) (a-b)(a^2+b^2 + ab) (a^2+b^2 - ab)