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)