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Year 10 Interactive Maths - Second Edition


Difference of Two Squares

Expand the binomial product (a + b)(a - b) using the Distributive Law and collect like terms.

Note that the expansion of (a + b)(a - b) yields the difference of two squares in a squared less b squared.

a squared less b squared equals (a + b)(a - b)

An expression in the form of a squared less b squared is called the difference of two squares.


Example 6

Expand the binomial product (x + y)(x - y)

Solution:

The binomial product (x + y)(x - y) is expanded using the Distributive Law.


Example 7

Example 7 involves expanding two binomial products.  You can expand the product using either the Distributive Law or the formula for the difference of two squares.

Solution:

Expanding the binomial product (x + 7)(x - 7) using the Distributive Law.

Alternatively, we can use the formula:

The difference of two squares formula.

as shown below.

Expanding the binomial product (x + 7)(x - 7) using the Difference of Two Squares formula.

Expanding the binomial product (4x - 5)(4x + 5) using the Distributive Law.

Alternatively, we can use the formula:

The difference of two squares formula.

as shown below.

Expanding the binomial product (4x - 5)(4x + 5) using the Difference of Two Squares formula.


Key Terms

difference of two squares


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