The formula is known as the difference of two squares. It is often helpful for simplifying arithmetic problems by using algebraic expressions.
In the formula, and represent any real numbers, variables, or expressions. The left side of the equation is an algebraic expression with two parts, one with the sum of and and the other with the difference between and . The right side of the equation represents the difference between the squares of and .
When multiplying the algebraic expression using the distributive property:
The middle terms, and , cancel each other out, resulting in the simplified form .
Let’s look at an example to see how this can be applied to a calculation
Example: Multiply 97 and 103
Using the difference of two squares formula, we can rewrite this multiplication as:
Notice that both expressions are in the form . In this case, and . Now, we can apply the difference of two squares formula:
Calculate the squares:
Thus, the product of 97 and 103 is 9991.
Let’s look at some more examples.
Example 1: Multiplying two numbers
Example 2: Squaring a number
Example 3: Difference of squares in multiplication
Example 4: Applying the difference of squares to various calculations
Find the value of the following: