Chemistry, asked by apoorvshukla185, 10 months ago

factorize. 64 a6–b6​

Answers

Answered by Anonymous
5

Answer:

a6+b6

Final result :

(a2 + b2) • (a4 - a2b2 + b4)

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "b6" was replaced by "b^6". 1 more similar replacement(s).

Step by step solution :

Step 1 :

Trying to factor as a Sum of Cubes :

1.1 Factoring: a6+b6

Theory : A sum 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 : a6 is the cube of a2

Check : b6 is the cube of b2

Factorization is :

(a2 + b2) • (a4 - a2b2 + b4)

Trying to factor a multi variable polynomial :

1.2 Factoring a4 - a2b2 + b4

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

Factorization fails

Final result :

(a2 + b2) • (a4 - a2b2 + b4)

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