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The simplify command is used to apply simplification rules to an expression.

The simplify routine searches the expression for function calls, square roots, radicals, and powers and invokes the appropriate simplification procedures.

$\mathrm{simplify}\left(4^{\frac{1}{2}}+3\right)$

$5$

$\mathrm{simplify}\left(\exp \left(a+\ln \left(b\exp \left(c\right)\right)\right)\right)$

$b{\ⅇ}^{c+a}$

$\mathrm{simplify}\left({\sin \left(x\right)}^2+\ln \left(2x\right)+{\cos \left(x\right)}^2\right)$

$\ln \left(2\right)+\ln \left(x\right)+1$

When trig is specified as the second argument, only the trigonometric expressions are simplified.

$\mathrm{simplify}\left({\sin \left(x\right)}^2+\ln \left(2x\right)+{\cos \left(x\right)}^2\,\mathrm{trig}\right)$

$\ln \left(2x\right)+1$

When you use the assume=property option as the last argument, all the indeterminate variables in expr are assumed to have the property when simplifying the expression. In the following example, x is assumed to be positive. For more information, see the simplify/details page.

$\mathrm{simplify}\left(\mathrm{sqrt}\left(x^2\right)\,\mathrm{assume}=\mathrm{positive}\right)$

$x$

The command simplify can perform simplification with respect to side relations. For details, see simplify/siderels .

$\mathrm{eqns}≔\left\{{\sin \left(x\right)}^2+{\cos \left(x\right)}^2=1\right\}\:$

$e≔{\sin \left(x\right)}^3-11{\sin \left(x\right)}^2\cos \left(x\right)+3{\cos \left(x\right)}^3-\sin \left(x\right)\cos \left(x\right)+2$

$e≔{\sin \left(x\right)}^3-11{\sin \left(x\right)}^2\cos \left(x\right)+3{\cos \left(x\right)}^3-\sin \left(x\right)\cos \left(x\right)+2$

$\mathrm{simplify}\left(e\,\mathrm{eqns}\right)$

$14{\cos \left(x\right)}^3-{\cos \left(x\right)}^2\sin \left(x\right)+\left(-\sin \left(x\right)-11\right)\cos \left(x\right)+\sin \left(x\right)+2$

$\mathrm{simplify}\left(e\,\mathrm{eqns}\,\left[\sin \left(x\right)\,\cos \left(x\right)\right]\right)$

$14{\cos \left(x\right)}^3-{\cos \left(x\right)}^2\sin \left(x\right)+\left(-\sin \left(x\right)-11\right)\cos \left(x\right)+\sin \left(x\right)+2$

Simplify with respect to cos(x) first.

$\mathrm{simplify}\left(e\,\mathrm{eqns}\,\left[\cos \left(x\right)\,\sin \left(x\right)\right]\right)$

$\left(-14{\sin \left(x\right)}^2-\sin \left(x\right)+3\right)\cos \left(x\right)+{\sin \left(x\right)}^3+2$