Modeling Polynomials

Key:

$(x+1)^2$

Expanded = $(x+1)(x+1)$

Simplified = $(x^2+2x+1)$

Explanation = First I expanded the expression. Since $4^2$ = 4×4, then $(x+1)^2$ has to equal $(x+1)(x+1)$ . Then I simplified the expression using the FOIL method. First – (x)(x) = $x^2$ , outside – (x)(1) = x, inside (x)(1), and then last = 1×1. Then I added them up.

$(x-1)^2$

Expanded = $(x-1)(x-1)$

Simplified = $(x^2-2x+1)$

Explanation = For this one, I expanded it the same way as the first example, and used the FOIL method again.

$(x+1)(x-1)$

Simplified = $(x^2-1)$

Explanation = This one was already expanded, so I only had to use the FOIL method.

$(x-1)^3$

This image isn’t what it would actually look like, because algebra tiles can only work for two dimensional shapes. As soon as we cube it, it would become third dimensional, so this diagram only shows the expression as power of 2. This would be the first step of the equation, then you’d have to multiply this answer to (x-1) again to get your final answer.

Expanded = $(x-1)(x-1)(x-1)$

Simplified = $(x^2-2x+1)(x-1)$

$(x^3-3x^2+3x-1)$

Explanation = First I expanded the expression. Then I multiplied two of the (x-1)’s together, and then multiplied that answer to the last (x-1).

Modeling Polynomials

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