Answer :
Let's simplify the expression [tex]\(7x^2(6x + 3x^2 - 4)\)[/tex] step by step. We'll distribute [tex]\(7x^2\)[/tex] to each term inside the parentheses.
1. Distribute to the first term [tex]\(6x\)[/tex]:
[tex]\[
7x^2 \times 6x = 42x^3
\][/tex]
2. Distribute to the second term [tex]\(3x^2\)[/tex]:
[tex]\[
7x^2 \times 3x^2 = 21x^4
\][/tex]
3. Distribute to the third term [tex]\(-4\)[/tex]:
[tex]\[
7x^2 \times (-4) = -28x^2
\][/tex]
Now, let's combine all the terms we found:
- The term from the second step: [tex]\(21x^4\)[/tex]
- The term from the first step: [tex]\(42x^3\)[/tex]
- The term from the third step: [tex]\(-28x^2\)[/tex]
Putting it all together, the simplified expression is:
[tex]\[
21x^4 + 42x^3 - 28x^2
\][/tex]
Therefore, the correct simplification of the given expression is:
[tex]\[
21x^4 + 42x^3 - 28x^2
\][/tex]
This matches the option: [tex]\(21 x^4 + 42 x^3 - 28 x^2\)[/tex].
1. Distribute to the first term [tex]\(6x\)[/tex]:
[tex]\[
7x^2 \times 6x = 42x^3
\][/tex]
2. Distribute to the second term [tex]\(3x^2\)[/tex]:
[tex]\[
7x^2 \times 3x^2 = 21x^4
\][/tex]
3. Distribute to the third term [tex]\(-4\)[/tex]:
[tex]\[
7x^2 \times (-4) = -28x^2
\][/tex]
Now, let's combine all the terms we found:
- The term from the second step: [tex]\(21x^4\)[/tex]
- The term from the first step: [tex]\(42x^3\)[/tex]
- The term from the third step: [tex]\(-28x^2\)[/tex]
Putting it all together, the simplified expression is:
[tex]\[
21x^4 + 42x^3 - 28x^2
\][/tex]
Therefore, the correct simplification of the given expression is:
[tex]\[
21x^4 + 42x^3 - 28x^2
\][/tex]
This matches the option: [tex]\(21 x^4 + 42 x^3 - 28 x^2\)[/tex].
