What is the pattern used to factor the difference of perfect squares: LaTeX: a^2-b^2a 2 − b 2?

Here is their argument. given the obtuse angle x, we make a quadrilateral abcd with ∠dab = x, and ∠abc = 90◦, and ad = bc. say the perpendicular bisector to dc meets the perpendicular bisector to ab at p. then pa = pb and pc = pd. so the triangles pad and pbc have equal sides and are congruent. thus ∠pad = ∠pbc. but pab is isosceles, hence ∠pab = ∠pba. subtracting, gives x = ∠pad−∠pab = ∠pbc −∠pba = 90◦. this is a preposterous conclusion – just where is the mistake in the "proof" and why does the argument break down there?

At the many chips cookie company they are serious about the number of chocolate chips in their cookies they claim that each cookie hasn't c chips. if their claim is true there will be 200 chips in 10 cookies

Atransformation t : (x, y) (x-5,y +3) the image of a(2,-1) is