The expand command distributes products over sums. This is done for all polynomials.  For quotients of polynomials, only sums in the numerator are expanded; products and powers are left alone. See the normal command for dealing with quotients of polynomials.

The expand command also expands most mathematical functions, including AngerJ, BesselI, BesselJ, BesselK, BesselY, Beta, ChebyshevT, ChebyshevU, CylinderD, CylinderU, CylinderV, Dirac, Ei, GAMMA, GegenbauerC, HankelH1, HankelH2, HermiteH, JacobiAM, JacobiCD, JacobiCN, JacobiCS, JacobiDC, JacobiDN, JacobiDS, JacobiNC, JacobiND, JacobiNS, JacobiP, JacobiSC, JacobiSD, JacobiSN, JacobiTheta1, JacobiTheta2, JacobiTheta3, JacobiTheta4, JacobiZeta, KelvinBei, KelvinBer, KelvinHei, KelvinHer, KelvinKei, KelvinKer, LaguerreL, LegendreP, LegendreQ, LerchPhi, Psi, StruveH, StruveL, WeberE, WeierstrassP, WeierstrassPPrime, WeierstrassSigma, WeierstrassZeta, Zeta, abs, arccos, arccosh, arccot, arccoth, arccsc, arccsch, arcsec, arcsech, arcsin, arcsinh, arctan, arctanh, bernoulli, binomial, cos, cosh, cot, coth, csc, csch, csgn, dilog, erf, erfc, euler, exp, factorial, ln, pochhammer, polylog, sec, sech, signum, sin, sinh, tan, and tanh.

The optional arguments expr1, expr2, ..., exprn are used to prevent particular subexpressions in expr from being expanded. To prevent all expressions from being expanded, use the frontend command: frontend(expand, [expr]);

The expand command is extensible: if the procedure `expand/f` is defined, then the call expand(f(x)); calls `expand/f`(x);

$\mathrm{expand}\left(\left(x+1\right)\left(x+2\right)\right)$

$x^2+3x+2$

$\mathrm{expand}\left(\frac{x+1}{x+2}\right)$

$\frac{x}{x+2}+\frac{1}{x+2}$

$\mathrm{expand}\left(\frac{1}{\left(x+1\right)x}\right)$

$\frac{1}{\left(x+1\right)x}$

$\mathrm{expand}\left(\sin \left(x+y\right)\right)$

$\sin \left(x\right)\cos \left(y\right)+\cos \left(x\right)\sin \left(y\right)$

$\mathrm{expand}\left(\cos \left(2x\right)\right)$

$2{\cos \left(x\right)}^2-1$

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

${\ⅇ}^{a}b$

$\mathrm{expand}\left(\left(x+1\right)\left(y+z\right)\right)$

$xy+xz+y+z$

$\mathrm{expand}\left(\left(x+1\right)\left(y+z\right)\,x+1\right)$

$\left(x+1\right)y+\left(x+1\right)z$

$\mathrm{expand}\left(\ln \left(\frac{x}{{\left(1-x\right)}^2}\right)\right)$

$\ln \left(\frac{x}{{\left(1-x\right)}^2}\right)$

$\mathrm{assume}\left(x\,\mathrm{real}\right)$

$\mathrm{expand}\left(\ln \left(\frac{x}{{\left(1-x\right)}^2}\right)\right)$

$-\ln \left({\left(1-\mathrm{x~}\right)}^2\right)+\ln \left(\mathrm{x~}\right)$

$\mathrm{expand}\left(\mathrm{BesselJ}\left(2\,t\right)\right)$

$\frac{2\mathrm{BesselJ}\left(1\,t\right)}{t}-\mathrm{BesselJ}\left(0\,t\right)$

$\mathrm{expand}\left(\mathrm{LegendreQ}\left(2\,t\right)\right)$

$-\frac{\ln \left(t+1\right)}{4}+\frac{\ln \left(t-1\right)}{4}+\frac{3t^2\ln \left(t+1\right)}{4}-\frac{3t^2\ln \left(t-1\right)}{4}-\frac{3t}{2}$

$\mathrm{expand}\left(\mathrm{JacobiP}\left(3\,1\,\frac{1}{4}\,t\right)\right)$

$-\frac{307}{1024}-\frac{2247}{1024}t+\frac{1575}{1024}{t}^2+\frac{5075}{1024}{t}^3$

$\mathrm{ee}≔\left(a+b\right)z+\sin \left(a+b\right)+\exp \left(a+b\right)$

$\mathrm{ee}≔\left(a+b\right)z+\sin \left(a+b\right)+{\ⅇ}^{a+b}$

$\mathrm{expand}\left(\mathrm{ee}\right)$

$za+zb+\sin \left(a\right)\cos \left(b\right)+\cos \left(a\right)\sin \left(b\right)+{\ⅇ}^a{\ⅇ}^b$

$\mathrm{expand}\left(\mathrm{ee}\,\sin \left(a+b\right)\right)$

$za+zb+\sin \left(a+b\right)+{\ⅇ}^a{\ⅇ}^b$

$\mathrm{expand}\left(\mathrm{ee}\,\mathrm{op}\left(\mathrm{indets}\left(\mathrm{ee}\,\mathrm{specfunc}\left(\mathrm{anything}\,\exp \right)\right)\right)\right)$

$za+zb+\sin \left(a\right)\cos \left(b\right)+\cos \left(a\right)\sin \left(b\right)+{\ⅇ}^{a+b}$

$\mathrm{expand}\left(\mathrm{ee}\,\mathrm{op}\left(\mathrm{indets}\left(\mathrm{ee}\,\mathrm{specfunc}\left(\mathrm{anything}\,\left[\exp \,\sin \right]\right)\right)\right)\right)$

$za+zb+{\ⅇ}^{a+b}+\sin \left(a+b\right)$

$\mathrm{expand}\left(\mathrm{ee}\,\mathrm{op}\left(\mathrm{indets}\left(\mathrm{ee}\,\mathrm{function}\right)\right)\right)$

$za+zb+{\ⅇ}^{a+b}+\sin \left(a+b\right)$