Answer :
Sure! Let's simplify the expression [tex]\(7x^2(6x + 3x^2 - 4)\)[/tex] step by step.
1. Distribute [tex]\(7x^2\)[/tex] through each term inside the parentheses:
[tex]\[
7x^2 \cdot 6x + 7x^2 \cdot 3x^2 + 7x^2 \cdot (-4)
\][/tex]
2. Calculate the product for each term:
- For the first term: [tex]\(7x^2 \cdot 6x\)[/tex]
[tex]\[
7 \cdot 6 \cdot x^2 \cdot x = 42x^3
\][/tex]
- For the second term: [tex]\(7x^2 \cdot 3x^2\)[/tex]
[tex]\[
7 \cdot 3 \cdot x^2 \cdot x^2 = 21x^4
\][/tex]
- For the third term: [tex]\(7x^2 \cdot (-4)\)[/tex]
[tex]\[
7 \cdot (-4) \cdot x^2 = -28x^2
\][/tex]
3. Combine all the terms:
[tex]\[
21x^4 + 42x^3 - 28x^2
\][/tex]
So, the correct simplification of [tex]\(7x^2(6x + 3x^2 - 4)\)[/tex] is:
[tex]\(21x^4 + 42x^3 - 28x^2\)[/tex]
Among the given options:
- [tex]\(21x^4 - 42x^3 + 28x^2\)[/tex]
- [tex]\(42x^4 + 21x^3 - 3x^2\)[/tex]
- [tex]\(21x^4 + 42x^3 - 28x^2\)[/tex]
- [tex]\(42x^4 - 13x^3 + 11x^2\)[/tex]
The correct option is:
[tex]\(21x^4 + 42x^3 - 28x^2\)[/tex]
Therefore, the correct simplification is provided by the third option:
[tex]\[
\boxed{21x^4 + 42x^3 - 28x^2}
\][/tex]
1. Distribute [tex]\(7x^2\)[/tex] through each term inside the parentheses:
[tex]\[
7x^2 \cdot 6x + 7x^2 \cdot 3x^2 + 7x^2 \cdot (-4)
\][/tex]
2. Calculate the product for each term:
- For the first term: [tex]\(7x^2 \cdot 6x\)[/tex]
[tex]\[
7 \cdot 6 \cdot x^2 \cdot x = 42x^3
\][/tex]
- For the second term: [tex]\(7x^2 \cdot 3x^2\)[/tex]
[tex]\[
7 \cdot 3 \cdot x^2 \cdot x^2 = 21x^4
\][/tex]
- For the third term: [tex]\(7x^2 \cdot (-4)\)[/tex]
[tex]\[
7 \cdot (-4) \cdot x^2 = -28x^2
\][/tex]
3. Combine all the terms:
[tex]\[
21x^4 + 42x^3 - 28x^2
\][/tex]
So, the correct simplification of [tex]\(7x^2(6x + 3x^2 - 4)\)[/tex] is:
[tex]\(21x^4 + 42x^3 - 28x^2\)[/tex]
Among the given options:
- [tex]\(21x^4 - 42x^3 + 28x^2\)[/tex]
- [tex]\(42x^4 + 21x^3 - 3x^2\)[/tex]
- [tex]\(21x^4 + 42x^3 - 28x^2\)[/tex]
- [tex]\(42x^4 - 13x^3 + 11x^2\)[/tex]
The correct option is:
[tex]\(21x^4 + 42x^3 - 28x^2\)[/tex]
Therefore, the correct simplification is provided by the third option:
[tex]\[
\boxed{21x^4 + 42x^3 - 28x^2}
\][/tex]
