Question

How do you write `(4s+5)(7x^2-4s+3)` in standard form?

Answer 1

`28s^3+19s^2-8s+15`

Explanation:

Polynomial standard form means that the expression is written as a series of terms in descending degree sequence (where the "degree" of a term is the sum of the exponents of the variables in the term).

In the case of `(4s+5)(7x^2-4s+3)`
the main problem is to perform the multiplication so the expression appears as a series of terms (and not as the product of two series of terms).
There are several ways to perform this multiplication; here is one version:

#{:(underline(xx)," | ",underline(+7s^2),underline(-4s),underline(+3)), (+4s," | ",+28s^3,-16s^2,+12s), (underline(+5),underline(" | "),underline(+35s^2),underline(-20s),underline(+15)), (,28s^3,+19s^2,-8s,+15) :}#

Note that as calculated these terms are already in descending degree sequence and thus the result is in standard polynomial form.