How do you multiply $(a-b)(a-b)$ ?

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Answer 1 · 2015-08-07T17:18:58

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

We multiply each term as follows

$a(a)+(a)(-b)+(-b)(a)+(-b)(-b)$

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

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

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

Or you can use the FOIL method. This is the same thing but just visualizing differently.

FOIL stands for

First Outside Inside Last

First multiply the first terms in $(a-b)(a-b)$
$a(a)=a^2$

Now add the products of the Outside and Inside terms

$a^2+(a)(-b)+(-b)(a)=a^2-2ab$

Finally we add the product of the last terms

$a^2-2ab+(-b)(-b)=a^2-2ab+b^2$

How do you multiply (a-b)(a-b)(a-b)(a-b)?