Sure! Let's break down and solve the expression step by step: [tex]\((x + 10)(3x + 10)\)[/tex].
To express this as a trinomial, we need to use the distributive property (also known as the FOIL method for binomials), which involves multiplying each term in the first binomial by each term in the second binomial.
### Step-by-Step Solution:
1. First terms:
Multiply the first term of each binomial:
[tex]\[
x \cdot 3x = 3x^2
\][/tex]
2. Outer terms:
Multiply the first term of the first binomial by the second term of the second binomial:
[tex]\[
x \cdot 10 = 10x
\][/tex]
3. Inner terms:
Multiply the second term of the first binomial by the first term of the second binomial:
[tex]\[
10 \cdot 3x = 30x
\][/tex]
4. Last terms:
Multiply the second term of each binomial:
[tex]\[
10 \cdot 10 = 100
\][/tex]
Now we combine all these products:
[tex]\[
(x + 10)(3x + 10) = 3x^2 + 10x + 30x + 100
\][/tex]
Next, we need to combine the like terms (the terms involving [tex]\(x\)[/tex]):
[tex]\[
10x + 30x = 40x
\][/tex]
So, putting it all together, the trinomial form of the given expression is:
[tex]\[
3x^2 + 40x + 100
\][/tex]
Therefore, the expression [tex]\( (x + 10)(3x + 10) \)[/tex] simplified and expressed as a trinomial is:
[tex]\[
\boxed{3x^2 + 40x + 100}
\][/tex]
