︠72e43e8b-a383-4604-84a2-7753612cfe25i︠
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2.1. {3 {x}^{2} } + {5 x}+ {17 x}-{{x}^{2} }.
︡cd0e6f41-0033-436c-bb24-071f38a68687︡{"html": "\r\n2.1. {3 {x}^{2} } + {5 x}+ {17 x}-{{x}^{2} }.\r\n"}︡
︠3593b154-31f5-4509-896a-6240a9d55bb0︠
simplify(3*x^2+5*x +17*x-x^2)
︡383cb734-10a2-4fda-82d1-eea8e9c7df34︡{"html": "{2 {x}^{2} } + {22 x}"}︡
︠91d69d2f-e3c8-4810-bf95-647ff03f7fcci︠
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2.2. {{\left( x - 1 \right)} {\left( x - 1 \right)} \left( {2 x} - 3 \right)}.
︡4c75c7ab-faa2-4810-8561-b9176fb02b32︡{"html": "\r\n2.2. {{\\left( x - 1 \\right)} {\\left( x - 1 \\right)} \\left( {2 x} - 3 \\right)}.
\r\n"}︡
︠db42c127-7c66-4f93-bcf0-c942b5863edb︠
f=(x-1)*(x-1)*(2*x-3); simplify(f)
︡05e62219-090d-47d4-8117-7b8e670ed903︡{"html": "{{\\left( x - 1 \\right)}^{2} \\left( {2 x} - 3 \\right)}"}︡
︠ae163263-6feb-4f4d-9335-84c59e4a6ebe︠
f=(x-1)*(x-1)*(2*x-3); f.simplify()
︡cb8b0ea3-df48-42a5-a40c-5a2f6928bd33︡{"html": "{{\\left( x - 1 \\right)}^{2} \\left( {2 x} - 3 \\right)}"}︡
︠4808f9cd-06d7-4618-9834-ae4ac8c01005i︠
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2.3. : {{\left( x - 1 \right)} \left( {x}^{2} - 1 \right)}.
︡bc320174-1cc5-4f26-b964-47a61b1c41e1︡{"html": "\r\n2.3. : {{\\left( x - 1 \\right)} \\left( {x}^{2} - 1 \\right)}."}︡
︠bce97880-e1af-4d61-be7f-911de351ca0a︠
expand((x-1)*(x^2-1))
︡6ef15c56-6244-4363-8688-4635e9c70e4e︡{"html": "{x}^{3} - {x}^{2} - x + 1"}︡
︠b3d95aed-bc0b-4cc6-9aa1-cd96d74c5d4fi︠
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2.4. : {{3}{x}{\left( x - 6 \right)} -\left( {2}{x}^{2} - 14 \right)}.
︡d2af5d81-eb0d-4fec-bb7b-619502cde147︡{"html": "2.4. : {{3}{x}{\\left( x - 6 \\right)} -\\left( {2}{x}^{2} - 14 \\right)}."}︡
︠4b4897cf-c8f6-49f6-b682-45b53daf46de︠
a=3*x*(x-6)-(2*x^2-14); a
︡3088e9ec-b232-4fcb-a08e-606f778aa84a︡{"html": "{-2 {x}^{2} } + {{3 \\left( x - 6 \\right)} x} + 14"}︡
︠f94ed916-cec9-4fd4-b878-6805c48b1ffb︠
expand(a)
︡eea88104-ada0-4f76-b99f-fe83cb572997︡{"html": "{x}^{2} - {18 x} + 14"}︡
︠5de8bac8-d3ae-431b-bdad-056897375f04i︠
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2.5. : {{\left( x - 1 \right)} \left( {x}^{2} - {2}{x} + 2 \right)}.
︡d7e423e3-b7fc-4a80-962f-e0cbb454eda5︡{"html": "2.5. : {{\\left( x - 1 \\right)} \\left( {x}^{2} - {2}{x} + 2 \\right)}."}︡
︠6aa12bae-e27f-4f66-8166-a47b2afbc8ca︠
b=(x-1)*(x^2-2*x+2); b
︡c821abe0-3ac7-4fbd-b339-9269a2c83aee︡{"html": "{\\left( x - 1 \\right) \\left( {x}^{2} - {2 x} + 2 \\right)}"}︡
︠f9212cf1-bc86-4fb2-b412-46f11bad72b5︠
b.expand()
︡fe85be9a-28c9-4116-bf8f-1c4e71d939e0︡{"html": "{x}^{3} - {3 {x}^{2} } + {4 x} - 2"}︡
︠009d2083-1946-46de-9f8d-7e380d66f3a4i︠
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2.6. {{x}^{12}-1}.
︡b002baa4-83c8-4119-8b2a-9e9ca366e57f︡{"html": "2.6. {{x}^{12}-1}."}︡
︠a60a6671-21d9-4420-be17-610bece2632c︠
factor(x^12-1)
︡331c9f40-620e-4fb8-9b05-6e7d31ab4864︡{"html": "{{{{{\\left( x - 1 \\right) \\left( x + 1 \\right)} \\left( {x}^{2} + 1 \\right)} \\left( {x}^{2} - x + 1 \\right)} \\left( {x}^{2} + x + 1 \\right)} \\left( {x}^{4} - {x}^{2} + 1 \\right)}"}︡
︠dd0c91d0-a4f2-45ca-9591-9ac8e6f450bfi︠
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2.7. {{a}^{2}-{ab}-{4a}+{4b}}.
︡cfbea781-e9f2-49b5-a360-240bdefbe005︡{"html": "2.7. {{a}^{2}-{ab}-{4a}+{4b}}."}︡
︠04ac909a-91ea-41b9-a3c6-799849c3e094︠
var('a,b')
factor(a^2-a*b-4*a+4*b)
︡5c729e29-dca3-49af-806b-ffbde7edca38︡{"html": "{\\left( a - 4 \\right) \\left( a - b \\right)}"}︡
︠d0344a1a-782c-4951-967b-0f7f21e3e38di︠
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2.8. {{ax}+{ay}-{az}+{nx}+{ny}-{nz}}.
︡0b574c49-b1e3-4720-9515-3ac41f0d4a77︡{"html": "2.8. {{ax}+{ay}-{az}+{nx}+{ny}-{nz}}."}︡
︠a0483912-7108-425a-8e6b-64a3b5cfa84f︠
var('x,y,z,a,n')
︡2e16282b-22ee-4c5b-b8bb-401303516316︡{"html": "\\left(x, \n y, \n z, \n a, \n n\\right)"}︡
︠2009cc04-71e6-4320-927c-9adc561cd636︠
exp=a*x+a*y-a*z+n*x+n*y-n*z; exp
︡a9a2b6ac-79e8-4117-908f-a2ca41966b5d︡{"html": "{-n z} - {a z} + {n y} + {a y} + {n x} + {a x}"}︡
︠ecf06bde-bf96-4319-a99b-903c37ece2af︠
factor(exp)
︡d0e926ef-c280-41f3-aab6-44fe3f1419d8︡{"html": "{\\left( n + a \\right) \\left( -z + y + x \\right)}"}︡
︠ca32dfb4-8943-4145-850d-9693c72184e6i︠
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2.9. {\sqrt[3]{x}+{\frac{1}{8}}{\sin \left( {10 x} \right)}} {{x}={2}}.
︡57936559-0975-4c41-829f-5cc0b5359f6b︡{"html": "2.9. {\\sqrt[3]{x}+{\\frac{1}{8}}{\\sin \\left( {10 x} \\right)}} {{x}={2}}."}︡
︠33ec2bfc-c49b-4868-ab9a-6c7af537e10b︠
f(x)=x^(1/3)+1/8*sin(10*x); f(x)
︡d2aed752-a2a0-4927-99d1-237ba933cec4︡{"html": "\\frac{\\sin \\left( {10 x} \\right)}{8} + {x}^{\\frac{1}{3}} "}︡
︠0cbdb7de-482f-4909-88e0-78ea7a9a85bb︠
f(2)
︡62a77f52-d98b-4a98-845b-bd2e79cf17de︡{"html": "\\frac{\\sin \\left( 20 \\right)}{8} + {2}^{\\frac{1}{3}} "}︡
︠79a5fcf9-fa0c-4473-b543-23f424e2d566︠
RR(f(2))
︡80d60c98-b200-4d9f-9a6e-bcd0b536ac7c︡{"html": "1.37403920623583"}︡
︠081d8da1-ad03-43d5-ba74-0353caaa4319i︠
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2.10. {{a}^{2}-{ab}-{4a}+{4b}} {{b}={2}}.
︡3d995620-9228-4c73-8d0e-d47bd18330dc︡{"html": "2.10. {{a}^{2}-{ab}-{4a}+{4b}} {{b}={2}}."}︡
︠444ab3b5-88c5-404e-8080-80fbbded58da︠
g(a,b)=(a^2-a*b-4*a+4*b);g(a,b)
︡4be66700-6501-433e-9ff5-b9e3eaa78aa1︡{"html": "{-a b} + {4 b} + {a}^{2} - {4 a}"}︡
︠2e9199f9-4489-4cb9-8530-259559bddf7a︠
g(a,2)
︡92682589-092b-4749-8804-0b752546da79︡{"html": "{a}^{2} - {6 a} + 8"}︡