#### Answer

a) $4(x+5)(x-5)$
b) $4(x+5)(x-5)$
c) Both of the coefficients are perfect squares, which allows the polynomial to be factored two different ways.
d) No. 75 is not a perfect square, so the polynomial cannot be factored as done in part b.

#### Work Step by Step

a)
$4x^2-100 = 4(x^2-25) = 4(x+5)(x-5)$
b)
$4x^2-100 = (2x+10)(2x-10) = 4(x+5)(x-5)$