Question

Factorise 4x2 - 4a2x+ a4-b4

Answer 1

Answer:Final result :

 (a2 + b2) • (a + b) • (a - b)

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "b4"   was replaced by   "b^4".  1 more similar replacement(s).

Step by step solution :

Step  1  :

Trying to factor as a Difference of Squares :

1.1      Factoring:  a4-b4

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 :  a4  is the square of  a2

Check :  b4  is the square of  b2

Factorization is :       (a2 + b2)  •  (a2 - b2)

Step-by-step explanation: