There are several methods for multiplying polynomials, you can use an algebra tile model, area model or the distributing method.
The Algebra tile model is used when the polynomials are fairly low because if they are high, you will need lots of space to draw.
A rectangle is used to represent X, a large square is used to represent X2, and a small square represents 1.
You place the tiles in one bracket on the top and the other bracket on the side in a line, you also color the positive colors in and leave the negatives white or red.
Once you have that drawn out, you draw lines between all the spaces horizontally and vertically. You should usually get a mix of all three shapes.
If both tiles are the same color, you shade the answer tile in (positive), if they are coloured and white/red, you leave it blank/red (negative).
The Area model is better with larger numbers since you don’t need to draw everything out.
For an area model, you do write down the first bracket on the top of a square (each term gets its own column) and you write the same thing for the second bracket on the left of the square (it works best in alphabetical order and largest to smallest exponent).
Once you have the setup, you draw lines down all the columns, so it looks kind of like a tick tack toe board.
You fill out all the multiplication boxes like a “times table”.
When you are done, you should have all the terms, you can add the like terms together (simplify) and arrange it in alphabetical order and largest to smallest exponent.
The Distributing method works best when multiplying 2 binomials but can do any size as well.
This method required the least amount of space, since it is not a model.
It can also be called FOIL or claw because it looks like a claw.
It can be called FOIL because you are taking the first 2 numbers in the brackets and multiplying them, the outside 2 numbers, the inside 2 numbers and the last 2 numbers.
If you have more than 2 terms in each, you can draw lines between a number in the first bracket, and all the numbers in the second bracket, then you do the same with the second, third and fourth… number in the first bracket. You then multiply all the lines.
Once you have all the answers you can dd the like terms together (simplify) and arrange it in alphabetical order and largest to smallest exponent.