Question

(2a^3-b^3)^3 - b^9 solve the equation​

Answer 1

Answer:

Given,

(2a3 – b3)3 – b9

We know, (x – y)3 = x3 – y3 – 3xy(x – y)

Therefore,

= (2a3)3 – (b3)3 – 3(2a3)(b3)(2a3 – b3) – b9

= 8a9 – b9 – 6a3b3(2a3 – b3) – b9

= 8a9 – 12a6b3 + 6a3b6 – 2b9

= 2a9 – 2b9 + 6a9 – 12a6b3 + 6a3b6

= 2(a9 – b9) + 6a3(a6 – 2a3b3 + b6)

Now, we know: x3 – y3 = (x – y)(x2 + xy + y2) and

(x – y)2 = x2 – 2xy + y2

= 2(a3 – b3)(a6 + a3b3 + b3) + 6a3(a3 – b3)2

= 2(a – b)(a2 + ab + b2)(a6 + a3b3 + b6) + 6a3(a – b)2(a2 + ab + b2)2

= 2(a – b)(a2 + ab + b2)(a6 + a3b3 + b6 + 3a3(a – b)(a2 + ab + b2))

= 2(a – b)(a2 + ab + b2)( a6 + a3b3 + b6 + 3a3(a3 + a2b + ab2 – a2b – ab2 – b3)

= 2(a – b)(a2 + ab + b2)( a6 + a3b3 + b6 + 3a3(a3 – b3) )

= 2(a – b)(a2 + ab + b2)( a6 + a3b3 + b6 + 3a6 – 3a3b3 )

= 2(a – b)(a2 + ab + b2)(4a6 – 2a3b3 + b6)