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: 

$6x^2+7x+2$