Polynomial expansion (多項式の展開): \((x+1)(x+2)(x+3)(x+4)\)

Q:

\((x+1)(x+2)(x+3)(x+4)\)


A:

\(x^4+10x^3+35x^2+50x+24\)


Command:

$ gnuplot


Result:

G N U P L O T
Version 5.0 patchlevel 5    last modified 2016-10-02

Copyright (C) 1986-1993, 1998, 2004, 2007-2016
Thomas Williams, Colin Kelley and many others

gnuplot home:     http://www.gnuplot.info
faq, bugs, etc:   type "help FAQ"
immediate help:   type "help"  (plot window: hit 'h')

Terminal type set to 'x11'


Command:

gnuplot> set zeroaxis lw 1 lt -1
gnuplot> set xr[-5:5]
gnuplot> set yr[-2.4:3.2]
gnuplot> set xtics 1
gnuplot> set ytics 1
gnuplot> set terminal png
Terminal type set to 'png'


Result:

Options are 'nocrop enhanced size 640,480 font "arial,12" '


Command:

gnuplot> set output 'polynomial.png'
gnuplot> plot x**4+10*x**3+35*x**2+50*x+24 lw 3


Output file:

polynomial.png

Polynomial expansion (多項式の展開): \((x+2a-3)^2\)

Q:

\((x+2a-3)^2\)

A:

\(x^2+4ax-6x+4a^2-12a+9\)

Polynomial expansion (多項式の展開):\((x-7+1)(x+y-1)\)

Q:

\((x-7+1)(x+7-1)\)

A:

\(x^2-y^2+2y-1\)

Polynomial expansion (多項式の展開): \((2x+1)(3x+2)\)

Q:

 \((2x+1)(3x+2)\)


A: 

\(6x^2+7x+2\)