Question

Factor the following polynomial completely
208p^2-325q^2

Answer 1

208 = 2 * 2 * 2 * 2 * 13 so sqrt208 = 4sqrt13
325 = 5 * 5 * 13 = 5sqrt13 so sqrt325 = 5sqrt13

208p^2-325q^2 = (4sqrt3p + 5sqrt13q)(4sqrt3p - 5sqrt13q)

Answer 2

i used the identity
a^2 - b^2 = (a + b)(a - b)