The product of (a+b)² is equal to a²+2ab+b².
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By definition of exponentiation, [tex](a+b)^2[/tex] is equal to [tex](a+b)[/tex] multiplied by itself two times, or:
[tex](a+b)^2=(a+b)(a+b)[/tex]
In order to find the product, we will use the FOIL method to expand and simplify.
[tex](a+b)(a+b)=\underbrace{a(a)}_{F}+\underbrace{a(b)}_{O}+\underbrace{b(a)}_{I}+\underbrace{b(b)}_{L}[/tex]
[tex](a+b)(a+b)=a^2+ab+ab+b^2[/tex]
[tex](a+b)(a+b)=\boxed{a^2+2ab+b^2}[/tex]
Therefore, the product of (a+b)² is equal to a²+2ab+b².
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Hope it helps.
