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

Mar 4, 2017

$28 {s}^{3} + 19 {s}^{2} - 8 s + 15$

#### 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 $\left(4 s + 5\right) \left(7 {x}^{2} - 4 s + 3\right)$
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.