Use the binomial theorem to find the 3rd term of (x+3y)^7

(a)

A square is formed.

(b)

A rectangle is obtained.

(c)

A triangle is formed.

Step-by-step explanation:

We have to tell different cross sections that are obtained on slicing a cube in different ways.

(a)

A slice through the center, parallel to a side.

( As the slicing is done parallel to the base and the cube is sliced from the center hence we will obtain the figure similar to it's base or top i.e. square)

Hence, a square is obtained.

( As the sides of a cube are squares)

(b)

A slice that cuts through the left top edge and the right bottom edge.

i.e. the slicing is done across the diagonal of a cube hence we will obtain the rectangle with dimension as one side which has measure same as the diagonal of a cube and the other side which has measure same as the measure of side of square.

Hence, a rectangle is obtained.

(c)

A slice that cuts across a corner through three sides of the cube.

This slicing will form a triangle whose three sides are the three sides of the cube through which slicing is done.