# How do you multiply #(3x + 4)(2x + 3)#?

##### 1 Answer

#### Explanation:

Most simple transformations of algebraic expressions are based on a set of laws:

*Commutative law* of addition:

*Associative law* of addition:

*Commutative law* of multiplication:

*Associative law* of multiplication:

*Distributive law* of multiplication over addition:

and, derived from it and from *commutative law*, the second form:

(The *distributive law* is often referred to as "opening the parenthesis")

Also, let's recall the rule of precedence: multiplication and division should be performed first, left to right, then addition and subtraction are performed with intermediary results, also left to right.

Using the *distributive law* in its first form for

we can write:

The first component, using the same *distributive law* in its second form, is

which, using the *commutative* and *associative laws* of multiplication, equals to

The second component, using the same laws can be transformed into

Adding together these two components in their final forms, we get:

This can be simplified further using the *distributive law* to two elements with

That results in the final form for our expression: