factorise 64-a^3b^3
Answers
Answer:
(ab - 4) • (a2b2 + 4ab + 16)
Step-by-step explanation:
Step 1 :
Trying to factor as a Difference of Cubes:
1.1 Factoring: a3b3-64
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 :
(ab - 4) • (a2b2 + 4ab + 16)
Trying to factor a multi variable polynomial :
1.2 Factoring a2b2 + 4ab + 16
Try to factor this multi-variable trinomial using trial and error
Factorization fails
Final result :
(ab - 4) • (a2b2 + 4ab + 16)
Answer:
hey Mate ! here is your answer.
