Algebra tiles multiplying

$(x+1)^2$

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

$=x^2+2x+1$

For the expansion of $(x+1)^2$ ,I multiplied $(x+1)$ by itself twice, then used the distributive property to simplify my expression.

$(x-1)^2$

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

$=x^2-2x+1$

For the expansion of $(x-1)^2$ ,I multiplied $(x-1)$ by itself twice, then used the distributive property to simplify my expression.

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

$=x^2-x+x-1$

$=x^2-1$

For the simplified expression of $(x+1)(x-1)$ ,I started off by distributing the variables in both of the brackets, combined the like terms, and came up with the simplified expression.

$(x-1)^3$ wasn’t possible to model with the tiles I had. I could only solve this algebraically.

$=(x-1)^3$

Formula for $(a-b)^3$

$a^3-3a^2b+3ab^2-b^3$

Therefore,

$(x-1)^3$

$=x^3-3x^2+3x-1$

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