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Multiplying Binomials Using the Punnett Rectangle

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You can multiply multiple binomials together using the Punnett Rectangle. To do that multiply the first two binomials together, then take the product and multiply it by the next binomial, and so on. The following example will help illustrate this:

Example 1 - Multiplying Binomials Using the Punnett Square

We'll start by first multiplying (x - 1) by (x - 2) using a Punnett Rectangle (which is a square to start):

x -1
x x2 -x
-2 -2x 2

We'll then combine our like terms to get: x2 - 3x + 2, this will form the top part of our next Punnett Rectangle and the next binomial will be the side:

x2 -3x 2
x x3 -3x2 2x
-3 -3x2 9x - 6

We can combine like terms to get x3 - 6x2 + 11x - 6.

Example 2 - Multiplying Binomials Using the Punnett Square

Let's look at another example:

We'll start by using the Punnett Rectangle to multiply (x - 1) by (x + 1).

x -1
x x2 -x
1 x -1

In this case the -x and x cancel out so we get x2 - 1, we can use that for the top of our new Punnett Rectangle:

x2 -1
2x 2x3 -2x
-2 -2x2 2

Therefore, we have 2x3 - 2x2 - 2x + 2 for our solution.