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5.1 Mathematical Manipulations • 149trig_expr := sin(x) cos(x) + sin(x) + y sin(x)> collect( trig_expr, sin(x) );(cos(x) + 1 + y) sin(x)> DE := diff(f(x),x,x)*sin(x) - diff(f(x),x)*sin(f(x))> + sin(x)*diff(f(x),x) + sin(f(x))*diff(f(x),x,x);DE := ( d2 f(x)) sin(x) − ( dddx 2 dxf(x)) sin(f(x)) + sin(x) (dx f(x))+ sin(f(x)) ( d2dx 2 f(x))> collect( DE, diff );(−sin(f(x)) + sin(x)) ( dd2f(x)) + (sin(x) + sin(f(x))) (dx dx 2 f(x))You cannot collect on sums or products.> big_expr := z*x*y + 2*x*y + z;big_expr := z x y + 2 y x + z> collect( big_expr, x*y );Error, (in collect) cannot collect y*xInstead, make a substitution before you collect. In the preceding case,substituting a dummy name for x*y, then collecting on the dummy nameproduces the desired result.> subs( x=xyprod/y, big_expr );z xyprod + 2 xyprod + z> collect( %, xyprod );(z + 2) xyprod + z> subs( xyprod=x*y, % );