(2x + 5y) (2x-5y) (4x^2 + 25y^2)

Answer 1

Expanding the given expression:

(2x + 5y) (2x - 5y) (4x^2 + 25y^2)

First, let's expand the first two terms using the FOIL method:
= (2x)*(2x) + (2x)*(-5y) + (5y)*(2x) + (5y)*(-5y)
= 4x^2 - 10xy + 10xy - 25y^2
= 4x^2 - 25y^2

Now, let's multiply this result by the third term:
= (4x^2 - 25y^2) * (4x^2 + 25y^2)
= 4x^2 * 4x^2 + 4x^2 * 25y^2 - 25y^2 * 4x^2 - 25y^2 * 25y^2
= 16x^4 + 100x^2y^2 - 100x^2y^2 - 625y^4
= 16x^4 - 625y^4

Therefore, the expanded expression is:

16x^4 - 625y^4