To simplify the expression [tex]\( 7 x^2(6 x + 3 x^2 - 4) \)[/tex], let's follow each step carefully:
1. Distribute [tex]\( 7 x^2 \)[/tex] to each term inside the parentheses:
[tex]\[
7 x^2 \cdot 6 x + 7 x^2 \cdot 3 x^2 - 7 x^2 \cdot 4
\][/tex]
2. Calculate each term separately:
- For the first term [tex]\( 7 x^2 \cdot 6 x \)[/tex]:
[tex]\[
7 x^2 \cdot 6 x = 42 x^3
\][/tex]
- For the second term [tex]\( 7 x^2 \cdot 3 x^2 \)[/tex]:
[tex]\[
7 x^2 \cdot 3 x^2 = 21 x^4
\][/tex]
- For the third term [tex]\( 7 x^2 \cdot 4 \)[/tex]:
[tex]\[
7 x^2 \cdot 4 = 28 x^2
\][/tex]
3. Combine the terms:
After distributing and simplifying each term, we get:
[tex]\[
42 x^3 + 21 x^4 - 28 x^2
\][/tex]
4. Rearrange the terms in standard polynomial form (highest degree first):
[tex]\[
21 x^4 + 42 x^3 - 28 x^2
\][/tex]
Thus, the correct simplification of [tex]\( 7 x^2(6 x + 3 x^2 - 4) \)[/tex] is:
[tex]\[
\boxed{21 x^4 + 42 x^3 - 28 x^2}
\][/tex]
