Aim: How do we solve diamond problems?

One way you can solve diamond problems is by putting the lowest number in addition and the highest in the multiplication. Find to factors that both numbers have in common and put both numbers in to equations; bring all the signs down with it.

Aim: How do we multiply rational expressions?

There are two methods when multiplying and solving for rational expressions. In some problems when multiplying rational expressions, there are two steps that you'll need to do in order to solve the problem.

     When multiplying rational expressions, you want the terms to be in simplest form. In order to do this, you'll have to use the diamond system and cross out all terms that are the same. Then you put the problem together as your final fantasy.

Aim: How do we multiply bionomials?

One method in multiplying bionomials is using the FOIL system which stands for first, inner, outter, last; and combining any like terms.
Example:  (2x+5)(x-2)
When using the FOIL method, you first distribute the 2x from the first equation in parenthesis to the second equation in parenthesis with the distrubutive property of multiplication and bring down the sighs:
(2x)(x)+(2x)(-2)= 2x^2-4x
Then from the first numbers in the parenthesis [(2x+5)] you use the same method, distrubtuive property of multiplication and mulitply 5 this time into the second equation and again, bring down the sighs:
(5)(x)+(5)(-2)=5x-10
You then combine the equation together: 2x^2-4x+5x-10
And combine any like terms as to being your final answer: 2x^2+x-10

Aim: How do we multiply polynomials?

One way we can multiply polynomials is by using the distrubutive property of multiplication and then combining any like terms.
Example: 2x(3x+1)
You distrubute the 2x on the out side of the parenthesis to 3x and 1 and bring down the sign
It would look like this : (2x)(3x)+(2x)(1)
Multiply  : 6x^2+2x