# Common Products

**General Binomial Product**

**Square of a Binomial**

**Difference of Squares**

Here, we have three equations for the product of two binomials, which are commonly used in algebra. The first formula is the **general formula** because the use of four distinct letters implies that all of the terms could be different. The second formula is for the **square of a binomial**, which is equivalent to the first formula with ** c = a** and

**. The third formula is called the**

*d = b***difference of squares**because of the right-hand side, and it is equivalent to the general formula with

**and**

*c = a***. The last two equations are just specializations of the first one.**

*d = -b*### Derivations

**General Binomial Product**

For the first equality, we apply the right-distributive property to get the right-hand side. Then we use the left-distributive property twice to get the second and final equality.

**Square of a Binomial**

To get the right-hand side of the first equality, we use the definition of an exponent. To get the second equality, we use the general formula that we derived above with ** c = a** and

**. For the third and final equality, we use the definition of exponents on the first and last terms and use commutativity and distributivity to combine the**

*d = b***terms.**

*ab***Difference of Squares**

For the first equality, we use the general formula with ** c = a** and

**to get the right-hand side. For the second inequality, we use the property that a product of an number and an additive inverse is the additive inverse of the product. For the third and final equality, we commutativity to say that**

*d = -b***and the definition of an additive inverse to cancel the**

*ba = ab***and**

*-ab***terms.**

*ab*