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simplify 1/2 (θ+1/2 sin(2θ))	simplify\:\frac{1}{2}(θ+\frac{1}{2}\sin(2θ))
expand x^2sin(x)-2(-xcos(x)+sin(x))+C	expand\:x^{2}\sin(x)-2(-x\cos(x)+\sin(x))+C
expand 25(2-pi)	expand\:25(2-π)
expand 2e^{3-t}+t^3+(t+1)^2	expand\:2e^{3-t}+t^{3}+(t+1)^{2}
expand (3x^4-10x^3+2x^2-3x+5)/((x-1)(3x+1))	expand\:\frac{3x^{4}-10x^{3}+2x^{2}-3x+5}{(x-1)(3x+1)}
expand (\sqrt[4]{-3125n^7})^6	expand\:(\sqrt[4]{-3125n^{7}})^{6}
expand (2(x^2-4))/(x^2-9)	expand\:\frac{2(x^{2}-4)}{x^{2}-9}
expand (4tan(x)+3)^2	expand\:(4\tan(x)+3)^{2}
simplify ((sqrt(m)-3)(sqrt(m)+5))/(m-25)	simplify\:\frac{(\sqrt{m}-3)(\sqrt{m}+5)}{m-25}
expand ((z+1)z)/(3(z^2-z+1))	expand\:\frac{(z+1)z}{3(z^{2}-z+1)}
expand csc^2(x)(sec^2(x)-cos^2(x))	expand\:\csc^{2}(x)(\sec^{2}(x)-\cos^{2}(x))
expand (-2e^{1/x}+x(2e^{1/x}-2))/(3x)	expand\:\frac{-2e^{\frac{1}{x}}+x(2e^{\frac{1}{x}}-2)}{3x}
lcm \delta(x-yy_{2}),y_{2}	lcm\:\delta(x-yy_{2}),y_{2}
expand (\sqrt[3]{x^2}+x^4)/(x^5)	expand\:\frac{\sqrt[3]{x^{2}}+x^{4}}{x^{5}}
expand ,4((1/2)+i((sqrt(3))/2))	expand\:,4((\frac{1}{2})+i(\frac{\sqrt{3}}{2}))
simplify 1/4 (1.2-1)+1/2	simplify\:\frac{1}{4}(1.2-1)+\frac{1}{2}
expand-sqrt(5)(-4-sqrt(2))	expand\:-\sqrt{5}(-4-\sqrt{2})
expand (12ab)/(a^2b^2)	expand\:\frac{12ab}{a^{2}b^{2}}
expand log_{4}(\sqrt[5]{(s^2t)/(16)})	expand\:\log_{4}(\sqrt[5]{\frac{s^{2}t}{16}})
expand (2,-4)y(6,10)	expand\:(2,-4)y(6,10)
expand 5sin^2(2)(ln(sin(2))+xcot(2))	expand\:5\sin^{2}(2)(\ln(\sin(2))+x\cot(2))
expand-1/((x-1)(x-2))	expand\:-\frac{1}{(x-1)(x-2)}
expand (x^2-x+y^2)dx+(2xy+e^{-y})dy	expand\:(x^{2}-x+y^{2})dx+(2xy+e^{-y})dy
expand (-3sin(x)+3sin(3x))^2+(3cos(x)-cos(3x)*3)^2	expand\:(-3\sin(x)+3\sin(3x))^{2}+(3\cos(x)-\cos(3x)\cdot\:3)^{2}
expand 2/((e^x-e^{-x))^2}	expand\:\frac{2}{(e^{x}-e^{-x})^{2}}
expand (e^x-2)e^x	expand\:(e^{x}-2)e^{x}
simplify 6(7d+1/2)	simplify\:6(7d+\frac{1}{2})
expand (sin^2(x))/((1+cos(x))^2)	expand\:\frac{\sin^{2}(x)}{(1+\cos(x))^{2}}
expand-1/2 x^2+2x-3/2+1/3 (x-1)^3	expand\:-\frac{1}{2}x^{2}+2x-\frac{3}{2}+\frac{1}{3}(x-1)^{3}
expand 3e^{3x}x^3ln(x+1)(x+1)	expand\:3e^{3x}x^{3}\ln(x+1)(x+1)
expand-3(x-1=-4)x+20	expand\:-3(x-1=-4)x+20
expand (-1-sqrt(37))^3	expand\:(-1-\sqrt{37})^{3}
expand (x-1)*x^{x/2}	expand\:(x-1)\cdot\:x^{\frac{x}{2}}
(d^2)/(dx^2)((y)(3x-y+3))	\frac{d^{2}}{dx^{2}}((y)(3x-y+3))
expand 1/(S(S^2+0.2S+1))	expand\:\frac{1}{S(S^{2}+0.2S+1)}
expand (x+y-1)dx+(y-x-5)dy	expand\:(x+y-1)dx+(y-x-5)dy
expand (x(4ydx+2xdy)+y^3(3yx+5xdy))(x^αy^β)	expand\:(x(4ydx+2xdy)+y^{3}(3yx+5xdy))(x^{α}y^{β})
expand (-3x^2-3x-10)/(x^2(-3x^2+24x))	expand\:\frac{-3x^{2}-3x-10}{x^{2}(-3x^{2}+24x)}
simplify \sqrt[3]{x}(\sqrt[3]{x^2}-8\sqrt[3]{x})	simplify\:\sqrt[3]{x}(\sqrt[3]{x^{2}}-8\sqrt[3]{x})
expand ((5x)/6-(4y)/3)^2	expand\:(\frac{5x}{6}-\frac{4y}{3})^{2}
expand (m+5,n-6)y(11,3)	expand\:(m+5,n-6)y(11,3)
expand (((x+h)^n-x^n))/h	expand\:\frac{((x+h)^{n}-x^{n})}{h}
expand t(e^{-3t}-t^2+1)	expand\:t(e^{-3t}-t^{2}+1)
expand (dx)/((4+x^2)^2)	expand\:\frac{dx}{(4+x^{2})^{2}}
expand (1+3cos(x))^2	expand\:(1+3\cos(x))^{2}
expand (3-x)/((x-2)^4)	expand\:\frac{3-x}{(x-2)^{4}}
expand x/((x^2+w^2)(x^2+4))	expand\:\frac{x}{(x^{2}+w^{2})(x^{2}+4)}
expand (cos(x)+cos(y))^2	expand\:(\cos(x)+\cos(y))^{2}
expand (x^m(x^m+1))/2	expand\:\frac{x^{m}(x^{m}+1)}{2}
simplify (1-2/(x+1))(3x^3)	simplify\:(1-\frac{2}{x+1})(3x^{3})
expand x^{2/3}(sqrt(x+1)-sqrt(x))	expand\:x^{\frac{2}{3}}(\sqrt{x+1}-\sqrt{x})
simplify x^2*(1/(2x^{1/2)}+1)	simplify\:x^{2}\cdot\:(\frac{1}{2x^{\frac{1}{2}}}+1)
expand δ,xiyy_{2}y_{3}(y_{4}-pi)	expand\:δ,xiyy_{2}y_{3}(y_{4}-π)
expand (3s-33)/((s^2+9)(s+2)(s-1))	expand\:\frac{3s-33}{(s^{2}+9)(s+2)(s-1)}
simplify 2(x^3-1/(x^3))	simplify\:2(x^{3}-\frac{1}{x^{3}})
expand sin(2)(x+h)	expand\:\sin(2)(x+h)
expand sin(3)(x^2+1)	expand\:\sin(3)(x^{2}+1)
expand 3000cos(0.5(x-1))+10000	expand\:3000\cos(0.5(x-1))+10000
expand (((2x+8))/6)^3	expand\:(\frac{(2x+8)}{6})^{3}
expand (1296(e-1))/(49)	expand\:\frac{1296(e-1)}{49}
expand 72((7pi)/6+1/4)	expand\:72(\frac{7π}{6}+\frac{1}{4})
expand (sqrt((x+h)^2+7)-sqrt(x^2+7))/h	expand\:\frac{\sqrt{(x+h)^{2}+7}-\sqrt{x^{2}+7}}{h}
expand (2x+1)/(4(x^2+x)^{5/4)}	expand\:\frac{2x+1}{4(x^{2}+x)^{\frac{5}{4}}}
simplify (-6sqrt(7)y-9sqrt(7))^2	simplify\:(-6\sqrt{7}y-9\sqrt{7})^{2}
expand (3X-4X^2)(6X+1)'\prime	expand\:(3X-4X^{2})(6X+1)\prime\:\prime
expand (16x^3-8x)(2x\sqrt[3]{x^2}+3)	expand\:(16x^{3}-8x)(2x\sqrt[3]{x^{2}}+3)
expand-(2x(x+1)^2)/3	expand\:-\frac{2x(x+1)^{2}}{3}
expand 3-sin(2x^2-3x-1)(4x-3)	expand\:3-\sin(2x^{2}-3x-1)(4x-3)
expand (3x^2+3y^2(dy)/(dx))(x^2+y^2)	expand\:(3x^{2}+3y^{2}\frac{dy}{dx})(x^{2}+y^{2})
expand (2(2n+3)(5n+3))/(3(5n+8)(2n+1))	expand\:\frac{2(2n+3)\cdot\:(5n+3)}{3(5n+8)\cdot\:(2n+1)}
expand f(x)(sin(x/2)=2+cos(x))	expand\:f(x)(\sin(\frac{x}{2})=2+\cos(x))
expand x+8x+16	expand\:x+8x+16
expand (cos(x)+asin(x))^2	expand\:(\cos(x)+a\sin(x))^{2}
expand derivative of (x^2+1arctan(x))-x	expand\:\frac{d}{dx}((x^{2}+1)\arctan(x))-x
expand (5/2 x+3/4 y)^2	expand\:(\frac{5}{2}x+\frac{3}{4}y)^{2}
expand facot(r)(-16x^3+33x^2-18x+1)	expand\:fa\cot(r)(-16x^{3}+33x^{2}-18x+1)
simplify 144x^5-3sqrt(x)(3+16x^{9/2})	simplify\:144x^{5}-3\sqrt{x}(3+16x^{\frac{9}{2}})
expand (2.1)(3x-4y+10=0)	expand\:(2.1)(3x-4y+10=0)
expand (e^{2x}y+xy+3z)(xy^2+ye^z+xz)	expand\:(e^{2x}y+xy+3z)(xy^{2}+ye^{z}+xz)
expand e^{2/x-c}*(-1/2 e^{(2+cx)/x}+c)	expand\:e^{\frac{2}{x}-c}\cdot\:(-\frac{1}{2}e^{\frac{2+cx}{x}}+c)
expand (16a^2+15b)/(20ab)	expand\:\frac{16a^{2}+15b}{20ab}
expand 2^6(x^{-2})^6	expand\:2^{6}(x^{-2})^{6}
expand 4xz+xsqrt(x^2+4(7.5-3z)^2)	expand\:4xz+x\sqrt{x^{2}+4(7.5-3z)^{2}}
expand A(s(s^2+16))	expand\:A(s(s^{2}+16))
expand 4/(s(s+3))	expand\:\frac{4}{s(s+3)}
expand (f\circ g)(x+5)(3x-4)	expand\:(f\circ\:g)(x+5)(3x-4)
d/(dv)((p)((p+(9.5)/(v^2))(v-9.8)))	\frac{d}{dv}((p)((p+\frac{9.5}{v^{2}})(v-9.8)))
expand (z^3+2z)/((z-a)^3)	expand\:\frac{z^{3}+2z}{(z-a)^{3}}
simplify (sqrt(5)x-sqrt(3))*(sqrt(5)x+sqrt(3))	simplify\:(\sqrt{5}x-\sqrt{3})\cdot\:(\sqrt{5}x+\sqrt{3})
expand (3x+pi/3)*((3pi)/4-2x)	expand\:(3x+\frac{π}{3})\cdot\:(\frac{3π}{4}-2x)
expand e^{x^3}(3x^2y-x^2)dx+e^{x^3}dy	expand\:e^{x^{3}}(3x^{2}y-x^{2})dx+e^{x^{3}}dy
expand (2(x+11))/((x-5)(x+3))	expand\:\frac{2(x+11)}{(x-5)(x+3)}
expand (x+y)left(x-y)	expand\:(x+y)left(x-y)
expand ((2x-1)/(2x))^3	expand\:(\frac{2x-1}{2x})^{3}
expand (3x^2-1/(x^3))^{10}	expand\:(3x^{2}-\frac{1}{x^{3}})^{10}
simplify-x(1-x/2)	simplify\:-x(1-\frac{x}{2})
expand (a/b+3)^2	expand\:(\frac{a}{b}+3)^{2}
expand 1/((x^2+3)(x-1))	expand\:\frac{1}{(x^{2}+3)(x-1)}
simplify (sqrt(7)-sqrt(t))(sqrt(7)+sqrt(t))	simplify\:(\sqrt{7}-\sqrt{t})(\sqrt{7}+\sqrt{t})
expand (d^2+1)(6sin(x))	expand\:(d^{2}+1)(6\sin(x))

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