How do you know when to rewrite square trinomials and difference of squares binomials as separate factors? Please stop copying and pasting old answers on the exact question there’s a reason why I’m asking it again

A trinomial is an expression that has three terms.

Square trinomial

A square trinomial is simply a perfect square trinomial, and it is represented as:

Difference of square binomials

This is easily identified because, the terms of the square binomials are perfect squares.

The difference of square binomials is represented as:

Sums and difference of cubes

When cubes are added or subtracted, they can be expressed using the following

--- sum of cubes

--- difference of cubes

Step-by-step explanation:

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.