# The square of the difference of two expressions is equal to the square of the first minus twice the product of the first and the second plus the square of the second.

**Important!**

Skip to content
# The square of the difference of two expressions

# The square of the difference of two expressions is equal to the square of the first minus twice the product of the first and the second plus the square of the second.

**Important!**

**Derivation of the Formula **

**Step 1**

**Step 2**

**Step 3**

**Step 4**

**Step 5**

**Now we will prove the reverse, i.e. we will prove that:**

**Step 1**

**Step 2**

**Step 3**

**Step 4**

**Step 5**

**Step 6**

**Step 7**

# Similar topics

You are here:

- Home
- Algebra
- Formulas of Abridged Multiplication
- The square of the difference…

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

** **

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

** **

Expand the brackets:

** **

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

** **

Collect like terms and multiply the elements:

** **

As a result, we can derive:

** **

** **

Consider:

** **

Let us write in the form:

** **

Apply this to the expression under consideration:

** **

Simplify:

** **

Factorize the common factors; and put -b outside the second bracket:

** **

Factorize the expression (a-b):

** **

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 has been derived.

Table of the formulas of abridged multiplication

The square of a sum. Derivation of the formula

The difference of the squares. Derivation of the formula

The cube of the sum of two expressions. Derivation of the formula

The cube of the difference of two expressions. Derivation of the formula

The sum of the cubes of two expressions. Derivation of the formula

The difference of the cubes of two expressions. Derivation of the formula

How to use the abridged multiplication formulas

Abridged multiplication formulas with examples (Tasks 1-11)

Abridged multiplication formulas with examples (Tasks 12-22)

The use of the formula of the square of the difference for squaring large numbers

MATHVOX

Go to Top
This site uses cookies to help you work more comfortably. By continuing to browse the pages of the site, you agree to the use of cookies. If you need more information, please visit the Privacy Policy page. Agree

Privacy & Cookies Policy

Don`t copy text!