Question

Factorize 81m^4 - (n-m)^4

Answer 1

Dear friend,

***The below process may look difficult, but write them down in the notebook to avoid confusion.***

To factorize the expression, we need to apply two algebraic identities,

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

(ii)(a-b)^2 = a^2 + b^2 - 2×a×b

Let's start factorizing it !

= 81m^4 - (n-m)^4

= [9m^2]^2 - [(n-m)^2]^2

= [9m^2 + (n-m)^2][9m^2 - (n-m)^2]

= [9m^2 + n^2 + m^2 - 2nm][(3m)^2-(n-m)^2]

= (10m^2 + n^2 - 2nm)(3m + n - m)(3m - n + m)

Answer: (10m^2 + n^2 - 2nm)(3m + n - m)(3m - n + m)

Hope it helps !!!

Answer 2

Answer:

Hey mate here is your answer