Answer :
Sure! Let's simplify the expression [tex]\[3 x^2(7 x^2 - 9)\][/tex]
Here’s a step-by-step solution:
1. Distribute [tex]\(3 x^2\)[/tex] inside the parentheses:
[tex]\[
3 x^2 \cdot (7 x^2 - 9)
\][/tex]
2. Multiply [tex]\(3 x^2\)[/tex] with each term inside the parentheses:
- Multiply [tex]\(3 x^2\)[/tex] by [tex]\(7 x^2\)[/tex]:
[tex]\[
3 x^2 \cdot 7 x^2 = 21 x^4
\][/tex]
- Multiply [tex]\(3 x^2\)[/tex] by [tex]\(-9\)[/tex]:
[tex]\[
3 x^2 \cdot (-9) = -27 x^2
\][/tex]
3. Combine the results from the multiplication:
[tex]\[
21 x^4 - 27 x^2
\][/tex]
So, the simplified expression is:
[tex]\[
21 x^4 - 27 x^2
\][/tex]
From the given choices:
- A. [tex]\(21 x^2 - 9\)[/tex]
- B. [tex]\(21 x^2 - 27 x^2\)[/tex]
- C. [tex]\(21 x^4 - 9\)[/tex]
- D. [tex]\(21 x^4 - 27 x^2\)[/tex]
The correct option is:
[tex]\[
\boxed{21 x^4 - 27 x^2}
\][/tex]
So, the correct answer is D. [tex]\(21 x^4 - 27 x^2\)[/tex].
Here’s a step-by-step solution:
1. Distribute [tex]\(3 x^2\)[/tex] inside the parentheses:
[tex]\[
3 x^2 \cdot (7 x^2 - 9)
\][/tex]
2. Multiply [tex]\(3 x^2\)[/tex] with each term inside the parentheses:
- Multiply [tex]\(3 x^2\)[/tex] by [tex]\(7 x^2\)[/tex]:
[tex]\[
3 x^2 \cdot 7 x^2 = 21 x^4
\][/tex]
- Multiply [tex]\(3 x^2\)[/tex] by [tex]\(-9\)[/tex]:
[tex]\[
3 x^2 \cdot (-9) = -27 x^2
\][/tex]
3. Combine the results from the multiplication:
[tex]\[
21 x^4 - 27 x^2
\][/tex]
So, the simplified expression is:
[tex]\[
21 x^4 - 27 x^2
\][/tex]
From the given choices:
- A. [tex]\(21 x^2 - 9\)[/tex]
- B. [tex]\(21 x^2 - 27 x^2\)[/tex]
- C. [tex]\(21 x^4 - 9\)[/tex]
- D. [tex]\(21 x^4 - 27 x^2\)[/tex]
The correct option is:
[tex]\[
\boxed{21 x^4 - 27 x^2}
\][/tex]
So, the correct answer is D. [tex]\(21 x^4 - 27 x^2\)[/tex].
