LEGEND:

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EXPRESSIONS:

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(x+1)^2

 

(x+1)(x+1)

 

x^2+x+x+1

 

x^2+2x+1

 

When expanding expressions that are to the power of 2 it helps to write them out. This helps because you can have a better understanding of what you are doing to multiply these two binomials together, and all the steps that are involved.

 

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(x-1)^2

 

(x-1)(x-1)

 

x^2-x-x+1

 

x^2-2x+1

 

This equation is almost the same as the former one, with the exception that that signs are different (+ and -). As mentioned before it is good to write out the expansion because it will help you avoid problems like confusing and mixing up the signs, and giving you an incorrect expansion.

 

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(x+1)(x-1)

 

x^2-x+x-1
x^2-1

 

With this expression, because the symbols are opposite, there is a rule we can use. “If the symbols are opposite but the values are the same the middle two multiplications will cancel each other out”. So instead of having to write out x^2-x+x-1 we already know that the two middle x’s will cancel each other out so we could skip writing out that step.

 

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(x-1)^3

 

(x-1)(x-1)(x-1)

 

(x^2-2x+1)(x-1)

 

x^3-3x^2+3x-1

 

You aren’t able to model expressions that are cubed, without using a 3D model, so I decided to model this expression in two steps. The first step I did was multiplying the binomials together, just like I did in the second example. From there I had a trinomial and a binomial left so I used the distributive property to multiply them together, and then simplified the expression.