Final answer:
The formula (a+b)(a-b) yields the difference of squares, which simplifies to a² - b² after canceling out the middle terms ab and -ab.
Step-by-step explanation:
The formula (a+b)(a-b) yields the difference of squares, which simplifies to a² - b² after canceling out the middle terms ab and -ab.
In algebra, the product of the sum and difference of two terms is known as the difference of squares. In this case, the sum is (a+b) and the difference is (a-b). To find the product, we can use the formula:
(a+b)(a-b) = a^2 - b^2
So, the product of (a+b) and (a-b) is a^2 - b^2.The product of the sum and difference of two terms (a+b)(a-b) is known as the difference of squares formula.
When you expand this, you multiply a by a to get a², a by -b to get -ab, b by a to get ab, and b by -b to get -b². Simplifying, the ab and -ab cancel each other out, leaving you with a² - b², which is the result of the difference of squares.