Algebra: Chapter 5-10, p 245
Multiplying Binomials: Special Products
We can use the FOIL or BOX methods to multiply binomials. There are however, 3 special cases that if you recognize them, will save you some work:
- `(A+B)(A-B)=A^2−B^2`
- `(A+B)(A+B)=A^2+B^2+2AB`
- `(A−B)(A−B)=A^2+B^2−2AB`
Remember, that A and B are the terms (monomials or constants) that we just plug in. If you forget these 3 cases, that’s OK, just FOIL or BOX the binomials and the answers are still the same.
Math-8: Chapter 8-1, p 372
Relations and Functions
A relation is a set of ordered pairs. The first coordinate (the x coordinate) is called the DOMAIN. The second coordinate (the y coordinate) is called the RANGE.
x=domain
y=range
A FUNCTION is a relation in which each element of the domain is paired with EXACTLY 1 ELEMENT in the range. Only 1 x-value for one y-value! One x cannot have multiple y points, like (2,4) and (2,6).
We can use the VERTICLE LINE TEST to determine if a relation is a FUNCTION. For each value of x, the vertical line test will show that the vertical line passes through NO MORE THAN 1 POINT ON THE GRAPH AT ANY ONE TIME.
Click here for some more words on functions, domain and range and pictures of the vertical line test in action.