Question

64-a^3 b^3 factories this ​

Answer 1

64a3-b3

Final result :

(4a - b) • (16a2 + 4ab + b2)

Step by step solution :

Step 1 :

Equation at the end of step 1 :

26a3 - b3

Step 2 :

Trying to factor as a Difference of Cubes:

2.1 Factoring: 64a3-b3

Theory : A difference of two perfect cubes, a3 - b3 can be factored into

(a-b) • (a2 +ab +b2)

Proof : (a-b)•(a2+ab+b2) =

a3+a2b+ab2-ba2-b2a-b3 =

a3+(a2b-ba2)+(ab2-b2a)-b3 =

a3+0+0+b3 =

a3+b3

Check : 64 is the cube of 4

Check : a3 is the cube of a1

Check : b3 is the cube of b1

Factorization is :

(4a - b) • (16a2 + 4ab + b2)

Trying to factor a multi variable polynomial :

2.2 Factoring 16a2 + 4ab + b2

Try to factor this multi-variable trinomial using trial and error

Factorization fails

Final result :

(4a - b) • (16a2 + 4ab + b2)

Answer 2

Answer:(4-ab)^3

Step-by-step explanation: