Question

Factor the expression completely. 625x4 - 256y4

Answer 1

Answer:

(625 • (x4)) -  28y4

 54x4 -  28y4 3.1      Factoring:  625x4-256y4  

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 - B2Note :  AB = BA is the commutative property of multiplication.

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

Check :  625  is the square of  25  

Check : 256 is the square of 16

Check :  x4  is the square of  x2  

Check :  y4  is the square of  y2  

Factorization is :       (25x2 + 16y2)  •  (25x2 - 16y2)  3.2      Factoring:  25x2 - 16y2  

Check :  25  is the square of  5  

Check : 16 is the square of 4

Check :  x2  is the square of  x1  

Check :  y2  is the square of  y1  

Factorization is :       (5x + 4y)  •  (5x - 4y)this is the answer: (25x2 + 16y2) •(5x + 4y) • (5x - 4y)