Let's solve the given expression step-by-step:
Given expression:
[tex]\[ 3m^2 \left(2m^2 - 4mn + n^2\right) \][/tex]
To simplify the expression, we need to distribute [tex]\(3m^2\)[/tex] through the polynomial inside the parentheses:
1. Distribute [tex]\(3m^2\)[/tex] to [tex]\(2m^2\)[/tex]:
[tex]\[ 3m^2 \cdot 2m^2 = 6m^4 \][/tex]
2. Distribute [tex]\(3m^2\)[/tex] to [tex]\(-4mn\)[/tex]:
[tex]\[ 3m^2 \cdot -4mn = -12m^3n \][/tex]
3. Distribute [tex]\(3m^2\)[/tex] to [tex]\(n^2\)[/tex]:
[tex]\[ 3m^2 \cdot n^2 = 3m^2n^2 \][/tex]
Now, combine all the distributed terms:
[tex]\[ 6m^4 - 12m^3n + 3m^2n^2 \][/tex]
Thus, the simplified form of the expression [tex]\(3m^2 \left(2m^2 - 4mn + n^2\right)\)[/tex] is:
[tex]\[ 6m^4 - 12m^3n + 3m^2n^2 \][/tex]
So, the final simplified expression is:
[tex]\[ 3m^2 \left(2m^2 - 4mn + n^2\right) = 6m^4 - 12m^3n + 3m^2n^2 \][/tex]
