x^2 + 81
we can factor this using difference of square binomials.
rewrite the equation:
x^2 - (-81)
factor:
(a^2 - b^2) = (βa^2 + βb^2)(βa^2 - βb^2)
(x^2 - (-81) = (x + β-81)(x - β-81)
we can remove the - from under the radical by multiplying it by i.
(x^2 - (-81) = (x + iβ81)(x - iβ81)
(x^2 - (-81) = (x + 9i)(x - 9i)
(x + 9i)(x - 9i)
we can check our answer by using foil:
x^2 - 9ix + 9ix - 81i^2
x^2 - 81^2
i^2 = -1
x^2 + 81