︠9a88fd78-e470-4e19-bc56-7c87974ae3bes︠ p1=sum([x^(25*i) for i in range(4)]) p2=sum([x^(5*i) for i in range(16)]) show(p1) show(p2) show(expand(p1*p2)) ︡08fbe9a9-f091-4a93-867c-26ce053315fb︡{"html":"
$\\displaystyle x^{75} + x^{50} + x^{25} + 1$
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$\\displaystyle x^{75} + x^{70} + x^{65} + x^{60} + x^{55} + x^{50} + x^{45} + x^{40} + x^{35} + x^{30} + x^{25} + x^{20} + x^{15} + x^{10} + x^{5} + 1$
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$\\displaystyle x^{150} + x^{145} + x^{140} + x^{135} + x^{130} + 2 \\, x^{125} + 2 \\, x^{120} + 2 \\, x^{115} + 2 \\, x^{110} + 2 \\, x^{105} + 3 \\, x^{100} + 3 \\, x^{95} + 3 \\, x^{90} + 3 \\, x^{85} + 3 \\, x^{80} + 4 \\, x^{75} + 3 \\, x^{70} + 3 \\, x^{65} + 3 \\, x^{60} + 3 \\, x^{55} + 3 \\, x^{50} + 2 \\, x^{45} + 2 \\, x^{40} + 2 \\, x^{35} + 2 \\, x^{30} + 2 \\, x^{25} + x^{20} + x^{15} + x^{10} + x^{5} + 1$
"}︡{"done":true}︡ ︠bd04f411-8ad0-4fe7-b5be-0100aac89004s︠ cookies=sum([x^(2*i) for i in range(1,5)]) brownies=x^2+x^3+x^4+x^5 bread=sum([x^(i) for i in range(2,9)]) show(cookies) show(brownies) show(bread) show(expand(cookies*brownies*bread)) ︡04d3c7c6-d3ab-4c48-bf01-75137272e804︡{"html":"
$\\displaystyle x^{8} + x^{6} + x^{4} + x^{2}$
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$\\displaystyle x^{5} + x^{4} + x^{3} + x^{2}$
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$\\displaystyle x^{8} + x^{7} + x^{6} + x^{5} + x^{4} + x^{3} + x^{2}$
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$\\displaystyle x^{21} + 2 \\, x^{20} + 4 \\, x^{19} + 6 \\, x^{18} + 8 \\, x^{17} + 10 \\, x^{16} + 12 \\, x^{15} + 13 \\, x^{14} + 13 \\, x^{13} + 12 \\, x^{12} + 10 \\, x^{11} + 8 \\, x^{10} + 6 \\, x^{9} + 4 \\, x^{8} + 2 \\, x^{7} + x^{6}$
"}︡{"done":true}︡ ︠c5d5fb63-34a3-43b6-840c-79420fba00de︠