#4.    Factor: 

restart;  

factor(`+`(`*`(5, `*`(`^`(x, 2))), `*`(10, `*`(x, `*`(y))), `*`(5, `*`(`^`(y, 2))), `*`(20, `*`(x)), `*`(20, `*`(y)), `-`(105)));  

`+`(`*`(5, `*`(`+`(x, y, 7), `*`(`+`(x, y, `-`(3)))))); (2.4.1)
 

 

factor(`/`(`*`(`+`(`*`(3, `*`(`^`(a, 2), `*`(b))), `-`(`*`(9, `*`(a, `*`(b)))))), `*`(`+`(`-`(`*`(84, `*`(`^`(a, 3), `*`(`^`(b, 3))))), `*`(`^`(a, 3))))));  

`+`(`-`(`/`(`*`(3, `*`(b, `*`(`+`(a, `-`(3))))), `*`(`^`(a, 2), `*`(`+`(`*`(84, `*`(`^`(b, 3))), `-`(1))))))); (2.4.2)
 

 

 

factor(`/`(`*`(`+`(`*`(`^`(x, 4)), `-`(`*`(2, `*`(`^`(x, 2), `*`(`^`(y, 2))))), `*`(`^`(y, 4)))), `*`(`+`(`*`(`^`(x, 2)), `*`(2, `*`(x, `*`(y))), `*`(`^`(y, 2))))));  

`*`(`^`(`+`(x, `-`(y)), 2)); (2.4.3)
 

 

 

factor(`+`(`/`(`*`(3, `*`(x)), `*`(`+`(`*`(4, `*`(y)), `-`(`*`(4, `*`(x)))))), `/`(`*`(`+`(`*`(`^`(x, 2)), `*`(5, `*`(x, `*`(y))))), `*`(`+`(`*`(4, `*`(`^`(x, 2))), `-`(`*`(4, `*`(`^`(y, 2))))))), `-`... 

`+`(`-`(`/`(`*`(x), `*`(y)))); (2.4.4)
 

 

 

factor(`/`(`*`(`+`(sqrt(x), `-`(`/`(`*`(`/`(1, 3)), `*`(sqrt(x)))))), `*`(sqrt(x))));  

`+`(`/`(`*`(`/`(1, 3), `*`(`+`(`*`(3, `*`(x)), `-`(1)))), `*`(x))); (2.4.5)
 

 

 

factor(`+`(`*`(exp(x), `*`(`+`(`*`(`^`(x, 2)), 1))), `*`(2, `*`(x, `*`(exp(x))))));  

`*`(exp(x), `*`(`^`(`+`(x, 1), 2))); (2.4.6)