What is the completely factored form of d4 − 81?
(d + 3)(d − 3)(d + 3)(d − 3)
(d2 + 9)(d + 3)(d − 3)
(d2 + 9)(d − 3)(d − 3)
(d2 + 9)(d2 − 9)

For this case we must factor the following expression:

Rewriting the expression:

We factor using the formula of the square difference:

Where:

So:

From the second term we have:

Finally, the factored expression is:

check the picture below.

well, the angle at the vertex d is clearly not a right-angle, let's check for the one at the vertex f which does look like,   however if it's indeed, that means ef is perpendicular to df, in which case their slopes will be negative reciprocal of each other.

so the negative reciprocal of the slope of ef is 1, however the slope of df is not 1, is 1/2, so nope, they're not perpendicular lines.