Certainly! Let's break down the process step-by-step to express [tex]\((x + 10)(3x + 10)\)[/tex] as a trinomial.
We start with the given expression:
[tex]\[
(x + 10)(3x + 10)
\][/tex]
To convert this into a trinomial, we need to perform the expansion by distributing each term in the first parenthesis to every term in the second parenthesis.
First, distribute [tex]\(x\)[/tex] to both terms in [tex]\((3x + 10)\)[/tex]:
[tex]\[
x \cdot (3x + 10) = x \cdot 3x + x \cdot 10 = 3x^2 + 10x
\][/tex]
Next, distribute [tex]\(10\)[/tex] to both terms in [tex]\((3x + 10)\)[/tex]:
[tex]\[
10 \cdot (3x + 10) = 10 \cdot 3x + 10 \cdot 10 = 30x + 100
\][/tex]
Now we combine all these terms together:
[tex]\[
3x^2 + 10x + 30x + 100
\][/tex]
Combine like terms, [tex]\(10x\)[/tex] and [tex]\(30x\)[/tex]:
[tex]\[
3x^2 + 40x + 100
\][/tex]
Thus, the trinomial expression of [tex]\((x + 10)(3x + 10)\)[/tex] is:
[tex]\[
\boxed{3x^2 + 40x + 100}
\][/tex]
