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#