Determine whether each statement makes sense or does not make sense, and explain your reasoning....

Step 1
Determine whether each statement makes sense or does not make sense, and explain your reasoning. Although ${\displaystyle 20x^3}$ appears in both ${\displaystyle 20x^3+8x^2\text{and}20x^3+10x}$, I’ll need to factor ${\displaystyle 20x^3}$ in different ways to obtain each polynomial’s factorization?
Step 2
We are given two expressions:
${\displaystyle 20x^3+8x^2}$
and ${\displaystyle 20x^3+10x}$
if we factorize them,
${\displaystyle 20x^3+8x^2=4x^2(5x+2)}$
and ${\displaystyle 20x^3+10x=10x(2x^2+1)}$
We see that factorization depends on each term of the expression, so although both expressions contain one common term, because of the other term both have different ways.

Step 1
Given:
${\displaystyle 20x^3+8x^2\text{and}20x^3+10x}$
Step 2
Yes! statement makes sense
${\displaystyle 20x^3+8x^2}$
Break terms:
${\displaystyle =2x\times 2x\times 5x+2x\times 2x\times 2}$
Take common out:
${\displaystyle =2x\times 2x(5x+2)}$
${\displaystyle =4x^2(5x+2)}$
Step 3
${\displaystyle 20x^3+10x}$
Take common out:
${\displaystyle =10x(2x^2+1)}$