100 write and simplify a polynomial expression for the volume of each figure.

disclaimer: if the answers are wrong it will be reported

Step-by-step explanation:

The picture #1:

It's a rectangular prism. The formula of a volume of a rectangular prism:

l - length

w - width

h - height

We have

Substitute:

Use the distributive property a(b + c) = ab + ac

and the FOIL: (a + b)(c + d) = ac + ad + bc + bd

The picture #2:

It's a cone. The fomula of a volume of a cone:

r - radius

h - height

We have:

Substitute:

Use (a + b)² = a² + 2ab + b²

Use the distributive property:

The picture #3:

It's a pyramid with a rectangle in the base. The formula of a volume of a rectangular pyramid:

a, b - edge of a base

h - height

We have

Substitute:

Use the distributive property and the FOIL.

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for