(1) The sum and difference of two terms can be expressed as the square of the first term minus the square of the second term, as shown in the formula (x + y)(x - y) = x^2 - y^2. (2) Several examples are provided to illustrate multiplying the sum and difference of terms, which results in the difference of the squares of the two terms. (3) Multiplying expressions like (x - 2)(x + 2), (2x + 5)(2x - 5), (3x + y)(3x - y), and (xy4 - 3)(xy4 + 3) follows the pattern of being equal to the difference of

1. Sum and Difference
of Two Squares
Ms. G. Martin

2. The sum and difference of two terms can be expressed as
the square of the first number minus the square of the second
number.
Thus, (x + y)(x – y) = x2 – y2

3. Example 1. Find the product of (x – 2)(x + 2).
• Using the FOIL Method, we have:
(x – 2)(x + 2) = x2 – 2x + 2x – 4
= x2 – 4
This special product is similar in the square of a binomial except that the signs of the
second terms are different.

4. Example 2. Find the product of (2x + 5)(2x – 5).
=(2x + 5)(2x – 5)
= 4x2 – 10x + 10x – 25
= 4x2 - 25

5. Example 3. Find the product of (3x + y)(3x – y)
= (3x + y)(3x – y)
= 9x2 – 3xy + 3xy – y2
= 9x2 – y2

6. Example 4. Find the product of (xy4 – 3)(xy4 + 3).
= (xy4 – 3)(xy4 + 3)
= (x2y8 – 9)
Notice that, as illustrated in these examples, multiplying the sum and
difference of two terms is equal to the difference of the squares of
the two terms.