Sure, let's simplify each term one by one.
First Term: [tex]\(3x \cdot 2x^2\)[/tex]
Begin by expanding the term:
[tex]\[ 3 \cdot x \cdot 2 \cdot x \cdot x \][/tex]
Now, combine the constant multipliers and the variables:
[tex]\[ (3 \cdot 2) \cdot (x \cdot x \cdot x) \][/tex]
Calculate the constants:
[tex]\[ 3 \cdot 2 = 6 \][/tex]
Combine the variables:
[tex]\[ x \cdot x \cdot x = x^3 \][/tex]
So, the first term simplifies to:
[tex]\[ 6x^3 \][/tex]
Second Term: [tex]\(3x \cdot 4x\)[/tex]
Begin by expanding the term:
[tex]\[ 3 \cdot x \cdot 4 \cdot x \][/tex]
Now, combine the constant multipliers and the variables:
[tex]\[ (3 \cdot 4) \cdot (x \cdot x) \][/tex]
Calculate the constants:
[tex]\[ 3 \cdot 4 = 12 \][/tex]
Combine the variables:
[tex]\[ x \cdot x = x^2 \][/tex]
So, the second term simplifies to:
[tex]\[ 12x^2 \][/tex]
Third Term: [tex]\(3x \cdot 9\)[/tex]
Begin by expanding the term:
[tex]\[ 3 \cdot x \cdot 9 \][/tex]
Combine the constant multipliers and the variable:
[tex]\[ (3 \cdot 9) \cdot x \][/tex]
Calculate the constants:
[tex]\[ 3 \cdot 9 = 27 \][/tex]
So, the third term simplifies to:
[tex]\[ 27x \][/tex]
Here is the final simplified form for each term:
1. [tex]\( 3x \cdot 2x^2 = 6x^3 \)[/tex]
2. [tex]\( 3x \cdot 4x = 12x^2 \)[/tex]
3. [tex]\( 3x \cdot 9 = 27x \)[/tex]
I hope this helps!
