Question

3a^2b-81a^4b^4 factorize​

Answer 1

Answer:

The answer is given below :

Now,

3 {a}^{7} b - 81 {a}^{4}  {b}^{4}  \\  \\  = 3ab( {a}^{6}  - 27 {a}^{3}  {b}^{3} ) \\   \\ = 3ab( { {(a}^{2} )}^{3}  -  { {(3ab)}^{3} }) \\  \\  = 3ab( {a}^{2}  - 3ab)( {( {a}^{2}) }^{2}  + ( {a}^{2}  \times 3ab) +  {(3ab)}^{2} ) \\  \\  = 3ab( {a}^{2}  - 3ab)( {a}^{4}  + 3 {a}^{3} b + 9 {a}^{2}  {b}^{2} )

which is the required factorization.

Step-by-step explanation: