Today we will look at an example of how you can find
one hundred and one cubed using the abbreviated multiplication formulas. In other words, how to raise
cube of 101 using the abbreviated multiplication formula.
The following cry for help was heard in the comments:
Help please, problem (example) from the physics and mathematics school (Russia), grade 8:
101^3
I don't understand how to solve this with abbreviated multiplication formulas.
It is very easy to cube the number
101  you need to type the number
101 on a calculator and multiply twice by the same number
101.
101^3=101*101*101=1030301
If you don't have a calculator at hand (you never know, the phone has just been stolen), then you can calculate on a piece of paper in a column (the picture will be at the end, like checking both the calculator and the formula).
Cube of 101
We apply the cube of sum formula.
The problem statement says that you need to find the cube of 101 using the abbreviated multiplication formula. According to math teachers, everyone should know these formulas. Naive. Where to find this formula?
You can search the Internet for a cube of sum. Google to help you. You can find these formulas in a reference book on mathematics, in a textbook on mathematics, you can ask a classmate who knows the formulas for abbreviated multiplication by heart. The formula for the abbreviated multiplication we need is called cube of sum. You will see it below.
And now the answer to the most tricky question: how to get the sum of numbers from one number? It is necessary to expand this number into terms. From the point of view of mathematics, the number of terms can be any, but ... I found the abbreviated multiplication formulas for raising a sum to a cube only for two and three terms. The formula for the cube of the sum of three terms is very complicated, I wish you never to face such a thing. But the cube of the sum of the two terms looks nice. The basic principle of expansion into terms for applying abbreviated multiplication formulas is that numbers can be easily multiplied in your head without using a calculator. For the number 101, the best option would be 101 = 100 + 1. 100 and 1 numbers is easy to multiply without a calculator. Let's see what we get.

Cube of 101 
I don't know about you, but I couldn't do without a piece of paper. Yes, I wrote everything down in a line, not a column, but nevertheless. And in conclusion, let's check our solution by multiplying in a column on a piece of paper.

Cube of 101 in a column on a piece of paper 
Well, something like this. Why do you need all this? So that you know that you can multiply not only on a calculator or in a column, but sometimes you can effectively use abbreviated multiplication formulas. If, of course, you know them.