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expand (5e^{2x}(2x-3))/(x^4)	expand\:\frac{5e^{2x}(2x-3)}{x^{4}}
simplify (sqrt(x)+3)(2sqrt(x)-5)	simplify\:(\sqrt{x}+3)(2\sqrt{x}-5)
expand 6xydx+(4y+9x^2)dy	expand\:6xydx+(4y+9x^{2})dy
expand ((7x^2-56x+105)*(-3x^2+108))x	expand\:((7x^{2}-56x+105)\cdot\:(-3x^{2}+108))x
expand-1/((3+s)^2(1+s))	expand\:-\frac{1}{(3+s)^{2}(1+s)}
expand e^{5t-20}h(t-4)	expand\:e^{5t-20}h(t-4)
simplify (sqrt(3))/2 (1+cos(4x))	simplify\:\frac{\sqrt{3}}{2}(1+\cos(4x))
expand (\H(x)-x)(x derivative of \H(x)-2\H(x))	expand\:(\H(x)-x)(x\frac{d}{dx}(\H(x))-2\H(x))
expand sec(x)(csc(x)+1)	expand\:\sec(x)(\csc(x)+1)
expand (567pi^2+18pi)/(2(63pi+2))	expand\:\frac{567π^{2}+18π}{2(63π+2)}
simplify cos^2(x)-cos(2x)(1/2 (1+cos(4x)))	simplify\:\cos^{2}(x)-\cos(2x)(\frac{1}{2}(1+\cos(4x)))
expand 16777216pi(1/2 ln(2+sqrt(5))+sqrt(5))	expand\:16777216π(\frac{1}{2}\ln(2+\sqrt{5})+\sqrt{5})
expand x(x^3+3x^2dx+3xdx^2+dx^3+1)	expand\:x(x^{3}+3x^{2}dx+3xdx^{2}+dx^{3}+1)
simplify (1.2b+4.32)((1.2b+4.32)/(b+7.59))^{2/3}	simplify\:(1.2b+4.32)(\frac{1.2b+4.32}{b+7.59})^{\frac{2}{3}}
expand (x-3)^2sqrt(x)	expand\:(x-3)^{2}\sqrt{x}
expand x^{2/a}(x^{2a}+1)	expand\:x^{\frac{2}{a}}(x^{2a}+1)
expand 3(te^t)(4+t)^2	expand\:3(te^{t})(4+t)^{2}
expand (5x^3(4e^{x/y}y^3-e^{x/y}xy^2))*y	expand\:(5x^{3}(4e^{\frac{x}{y}}y^{3}-e^{\frac{x}{y}}xy^{2}))\cdot\:y
expand (3(x+2))/4	expand\:\frac{3(x+2)}{4}
expand (0.5(3s+1))/(3s^2+s+2k)	expand\:\frac{0.5(3s+1)}{3s^{2}+s+2k}
expand ((x^2-3)^4sin(2x))/(5x-1)	expand\:\frac{(x^{2}-3)^{4}\sin(2x)}{5x-1}
expand 2y(y^2-x)dy	expand\:2y(y^{2}-x)dy
simplify (sqrt(x)-x^2)(1+sqrt(x))	simplify\:(\sqrt{x}-x^{2})(1+\sqrt{x})
expand (x-1)^3+1/2 x-2	expand\:(x-1)^{3}+\frac{1}{2}x-2
simplify 1/2 (1+log_{3}(2))	simplify\:\frac{1}{2}(1+\log_{3}(2))
expand x^{1/5}(x+1)	expand\:x^{\frac{1}{5}}(x+1)
expand (x^2-1-sqrt(3))^3	expand\:(x^{2}-1-\sqrt{3})^{3}
expand (y+1)dx-xdy	expand\:(y+1)dx-xdy
expand (2(a+b))/(a-b)	expand\:\frac{2(a+b)}{a-b}
simplify (sqrt(6-3x^3)+6)^2	simplify\:(\sqrt{6-3x^{3}}+6)^{2}
expand (-2sin(x)+1)(sin(x)+1)	expand\:(-2\sin(x)+1)(\sin(x)+1)
expand \sqrt[3]{4}(-2-\sqrt[3]{6})	expand\:\sqrt[3]{4}(-2-\sqrt[3]{6})
(\partial)/(\partial x)((z)((4x+3y)^2))	\frac{\partial\:}{\partial\:x}((z)((4x+3y)^{2}))
expand sqrt(11)(sqrt(2)-sqrt(7))	expand\:\sqrt{11}(\sqrt{2}-\sqrt{7})
expand AB(B^'+C)+AC	expand\:AB(B^{\prime\:}+C)+AC
expand (\frac{60)/(M+10)}{6/(M+10)}	expand\:\frac{\frac{60}{M+10}}{\frac{6}{M+10}}
expand (6+4cos(θ))^2	expand\:(6+4\cos(θ))^{2}
simplify (x-sqrt(x+2))(x+sqrt(x+2))	simplify\:(x-\sqrt{x+2})(x+\sqrt{x+2})
expand (1+i,-2i)-(a+bi,c+di)	expand\:(1+i,-2i)-(a+bi,c+di)
expand (6x)/((7x-10)(x+8))	expand\:\frac{6x}{(7x-10)(x+8)}
expand sqrt(3)(2sqrt(2)-sqrt(5))	expand\:\sqrt{3}(2\sqrt{2}-\sqrt{5})
expand (8x^3+12x^2+6x+1)(8x^3-36x^2=54x-27)	expand\:(8x^{3}+12x^{2}+6x+1)(8x^{3}-36x^{2}=54x-27)
expand 10(2+xsin(3x))^9*sin(3x)+3xcos(3x)	expand\:10(2+x\sin(3x))^{9}\cdot\:\sin(3x)+3x\cos(3x)
expand (-3,-1)y(2,3)	expand\:(-3,-1)y(2,3)
expand a(3,7)b(-5,-3)	expand\:a(3,7)b(-5,-3)
expand (1.7335*(s+7.91812)(s+0.001))/s	expand\:\frac{1.7335\cdot\:(s+7.91812)(s+0.001)}{s}
expand (1+tan^4(t/(12)))^3	expand\:(1+\tan^{4}(\frac{t}{12}))^{3}
simplify (t-1/2)(t^2-t+1/6)	simplify\:(t-\frac{1}{2})(t^{2}-t+\frac{1}{6})
simplify 1/((x+yi)^2-4)	simplify\:\frac{1}{(x+yi)^{2}-4}
expand-cos(v)sin(u)(2cos(v)+cos(v)cos(u))	expand\:-\cos(v)\sin(u)(2\cos(v)+\cos(v)\cos(u))
expand (1+t)(-1/2 ((t+1)^2-t^2))	expand\:(1+t)(-\frac{1}{2}((t+1)^{2}-t^{2}))
expand (sin(2t)+2sin(t))*(2sin(t)-2sin(2t))	expand\:(\sin(2t)+2\sin(t))\cdot\:(2\sin(t)-2\sin(2t))
expand (s+1)/((s+30)(s^2+s+1)(s+15))	expand\:\frac{s+1}{(s+30)(s^{2}+s+1)(s+15)}
expand (-3a^2b+8b)(-9a+5)^'	expand\:(-3a^{2}b+8b)(-9a+5)^{\prime\:}
expand 1/(\sqrt[5]{x+1)}	expand\:\frac{1}{\sqrt[5]{x+1}}
expand c(2,-3)	expand\:c(2,-3)
expand (5+7x)x^4e^{7x}	expand\:(5+7x)x^{4}e^{7x}
expand (7x-19)sin(x^2-4x+4)	expand\:(7x-19)\sin(x^{2}-4x+4)
simplify 1+(5((0.5)/s+0.5))/((2s+1)(0.1s+1))	simplify\:1+\frac{5(\frac{0.5}{s}+0.5)}{(2s+1)(0.1s+1)}
expand log_{7}(sqrt(49x^5))	expand\:\log_{7}(\sqrt{49x^{5}})
expand 1/((1+x)^8)	expand\:\frac{1}{(1+x)^{8}}
expand 2((4-t^6)(-2+t^6))	expand\:2((4-t^{6})(-2+t^{6}))
expand e^{2x}(2e^{2x}x^2+2e^{2x}x+e^{2x})	expand\:e^{2x}(2e^{2x}x^{2}+2e^{2x}x+e^{2x})
expand (2xy^3+4)dx+(3x^2y^2+8)dy	expand\:(2xy^{3}+4)dx+(3x^{2}y^{2}+8)dy
expand sin(2(x-pi))	expand\:\sin(2(x-π))
expand (8-x)ln(x+7)	expand\:(8-x)\ln(x+7)
expand (5cos(θ)-3sin(θ))^2	expand\:(5\cos(θ)-3\sin(θ))^{2}
expand (2x^3+2x^2-7x+12)/(x(x+3)(x-4)(x+2))	expand\:\frac{2x^{3}+2x^{2}-7x+12}{x(x+3)(x-4)(x+2)}
expand-(1+2e^x)y	expand\:-(1+2e^{x})y
simplify (5+2cos(x))(cos(x))	simplify\:(5+2\cos(x))(\cos(x))
simplify (x^9+3/4)(x^9-3/4)	simplify\:(x^{9}+\frac{3}{4})(x^{9}-\frac{3}{4})
expand (cos^2(x))^2+(sin^2(x))^2	expand\:(\cos^{2}(x))^{2}+(\sin^{2}(x))^{2}
expand (2x+6)/((x-3)(x+7))	expand\:\frac{2x+6}{(x-3)(x+7)}
expand sqrt((x+1)^2+y^2)	expand\:\sqrt{(x+1)^{2}+y^{2}}
expand (ay^5+by^4+1)/((y-1)^2)	expand\:\frac{ay^{5}+by^{4}+1}{(y-1)^{2}}
expand e^{-8x}(-8e^{-8x}x+e^{-8x})+8e^{-16x}x^2	expand\:e^{-8x}(-8e^{-8x}x+e^{-8x})+8e^{-16x}x^{2}
expand (pi(6-ln(7)))/2	expand\:\frac{π(6-\ln(7))}{2}
expand sqrt(3)(sqrt(11)+sqrt(5))	expand\:\sqrt{3}(\sqrt{11}+\sqrt{5})
expand (sqrt(x)-5)^4	expand\:(\sqrt{x}-5)^{4}
expand ((x+2)(7-x))/2	expand\:\frac{(x+2)(7-x)}{2}
expand (2+s^2)/((s^2+s-2)*s^2)	expand\:\frac{2+s^{2}}{(s^{2}+s-2)\cdot\:s^{2}}
expand (k+2)^2(k^2+4k+4)	expand\:(k+2)^{2}(k^{2}+4k+4)
expand (-x^3+2x)/((x-1)^2)	expand\:\frac{-x^{3}+2x}{(x-1)^{2}}
expand (1-5n^4)/((2n^2+1)^2)	expand\:\frac{1-5n^{4}}{(2n^{2}+1)^{2}}
d/(dy)((x)(x^2+y^2-2y-10))	\frac{d}{dy}((x)(x^{2}+y^{2}-2y-10))
expand sqrt(2)(1-sqrt(3))	expand\:\sqrt{2}(1-\sqrt{3})
simplify 2(5+sqrt(22))	simplify\:2(5+\sqrt{22})
expand (t+pi)^2	expand\:(t+π)^{2}
simplify (sqrt(x+1))(x+1)	simplify\:(\sqrt{x+1})(x+1)
expand (-8/5+3)(11/6+3)	expand\:(-\frac{8}{5}+3)(\frac{11}{6}+3)
expand tU(t-pi)	expand\:tU(t-π)
expand (x-sqrt(5))(x+3)(x-2)	expand\:(x-\sqrt{5})(x+3)(x-2)
expand (e^x-e^{-x})-ln(e^x+e^{-x})	expand\:(e^{x}-e^{-x})-\ln(e^{x}+e^{-x})
expand (d-e)(f-g)	expand\:(d-e)(f-g)
simplify (-2sqrt(3)-2i)^4	simplify\:(-2\sqrt{3}-2i)^{4}
expand-1/((x+4)(x+1)x^2)	expand\:-\frac{1}{(x+4)(x+1)x^{2}}
expand (x+2y-2)dx+(2x-y+3)dy	expand\:(x+2y-2)dx+(2x-y+3)dy
simplify (4x-1)(sqrt(6+7x))	simplify\:(4x-1)(\sqrt{6+7x})
expand (2pix)(2x+e^x)	expand\:(2πx)(2x+e^{x})
simplify 4(2cos^2(φ)-(sec^2(φ))/2)*sin(φ)	simplify\:4(2\cos^{2}(φ)-\frac{\sec^{2}(φ)}{2})\cdot\:\sin(φ)

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