# The square of a sum of two expressions is equal to the square of the first, plus twice the product of the first and second, plus the square of the second.

## Important!

The square of the sum formula shall be used for finding squares of large numbers.

## Derivation of the formula of the square of the sum. Method 1

Let us prove the formula from left to right, i.e. prove that:

## Step 1

The square of the expression is the expression mutiplied by itself:

## Step 2

Expand the brackets:

## Step 3

As the product remains the same by reordering its factors, then:

## Step 4

Collect like terms and multiply the elements:

## Step 5

As a result, we can derive:

Consider:

## Step 2

Let us write in the form:

## Step 3

Apply this to the expression under consideration:

Simplify:

Factorize:

## Step 6

Factorize the expression (a+b):

## Step 7

As a result of transformations we have a product of the expression by itself, and it is the square of this expression:

Hence, we have proved that:

The formula of the square of the sum has been derived.