Question

(x^8 - 4y^8) factorise ​

Answer 1

Step-by-step explanation:

STEP

1

:

Equation at the end of step 1

 (x8) -  22y8

STEP  

2

:

Trying to factor as a Difference of Squares:

2.1      Factoring:  x8-4y8  

Theory : A difference of two perfect squares,  A2 - B2  can be factored into  (A+B) • (A-B)

Proof :  (A+B) • (A-B) =

        A2 - AB + BA - B2 =

        A2 - AB + AB - B2 =

        A2 - B2

Note :  AB = BA is the commutative property of multiplication.

Note :  - AB + AB equals zero and is therefore eliminated from the expression.

Check : 4 is the square of 2

Check :  x8  is the square of  x4  

Check :  y8  is the square of  y4  

Factorization is :       (x4 + 2y4)  •  (x4 - 2y4)  

Trying to factor as a Difference of Squares:

2.2      Factoring:  x4 - 2y4  

Check : 2 is not a square !!

Ruling : Binomial can not be factored as the difference of two perfect squares.

Final result :

 (x4 + 2y4) • (x4 - 2y4)