Question 230181
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In general:

*[tex \LARGE \ \ \ \ \ \ \ \ \ \ (a+b)(c+d+e)\ =\ a(c+d+e)+b(c+d+e)\ =\ ac+ad+ae+bc+bd+be]


Even more generally:


*[tex \LARGE (a_1+a_2+\cdots+a_n)(b_1+b_2+\cdots+b_n)\ =\ a_1(b_1+b_2+\cdots+b_n)+a_2(b_1+b_2+\cdots+b_n)+\cdots+a_n(b_1+b_2+\cdots+b_n)]

*[tex \LARGE = a_1b_1+a_1b_2+\cdots+a_1b_n+a_2b_1+a_2b_2+\cdots+a_2b_n+\cdots+a_nb_1+a_nb_2+\cdots+a_nb_n]


Specifically:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ (x - 2) (x^4 + 3x -1)\ =\ x(x^4 + 3x -1) - 2(x^4 + 3x -1)\ = x^5+3x^2-x-2x^4-6x+2\ = x^5-2x^4+3x^2-7x+2]



John
*[tex \LARGE e^{i\pi} + 1 = 0]
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