Iincluded referenced equations through links to imgur - 30 points

1. simplify the following expressions. show all work for each.

(a)

(b)

(a)

(b)

Step-by-step explanation:

(a)

(3xy^3)(2x^3y)

(b)

This is just the rainbow method or as i like to call it the multiplication attack. All the terms in the first bracket fire themselves on the ones in the second. Each term attacks all the other terms once. Once they fire (multiply) they stick and can be added up. To make it easier i like to imagine them as squads.

(x^2 +2x +3)[x^2 -2x-4]

This can be expressed now as

(x^2 +2x +3)[x^2] + (x^2 +2x +3)[-2x] + (x^2 +2x +3)[-4]

Now to expand

x^4 + 2x^3 + 3x^2 -2x^3 -4x^2 - 6x -4x^2 - 8x - 12

Group like terms (same x powers)

(x^4) + (2x^3-2x^3) + (3x^2-4x^2-4x^2) + (- 6x-8x) + (-12)

Simplify

parallel and congruent

step-by-step explanation:

the movement of translation is linear.   these have the same translation because you are using the same rule for each point of the triangle so you will see the same slope being used to get from a point on the triangle to its image.

same slope!   you should think parallel when you see those 2 word together (well unless it's the same line but it can't be because we are coming from different points here)

congruent! because each point is being moved the same distance.