Algebra: Chapter 5 Review
Multiplying Polynomials
To multiply a monomial and a polynomial: multiply each term of the polynomial by the monomial
There are 3 techniques to multiply binomials:
- FOIL (FIRST, OUTSIDE, INSIDE, LAST – or its derivatives for trinomials)
- Multiply each term of a polynomial by EVERY OTHER TERM of the other polynomial
- The BOX method
- The BOX method, more like a rectangle with each term representing 1 side of an inner box. A binomial multiplied with a trinomial will be a BOX containing 2 x 3 number of smaller boxes inside it. Each term represents 1 edge in distance in the inner boxes.
- The old fashioned multiplication method outlined on page 249.
You get to chose which is most comfortable for you BUT REMEMBER THE BOX for Chapter 6!
Remember too, the shortcuts for special binomials:
- `(A+B)(A+B)=(A+B)^2=A^2+B^2+2AB`
- `(A−B)(A−B)=(A−B)2=A^2+B^2−2AB`
- `(A+B)(A−B)=A^2−B^2`
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Algebra 1a: Chapter 7, Lesson 1, page 304
Coordinates
Coordinates are defined as `(x, y)` where the x-axis runs left to right and the y-axis runs up and down. The origin is where the points `(0, 0)` exists. A fancy word for the x-axis is the abscissa and the y-axis is the ordinate. There are 4 quadrants:
- I – both x and y axis have positive value (upper right)
- II- x axis is negative and y axis is positive (upper left)
- III – both x and y axis have negative values (lower left)
- IV – x axis has positive value, while the y axis has negative value (lower right)