Answer :
Sure! Let's simplify the expression step by step.
We start with the expression:
[tex]\[ -9\left(7x^2 - 7x^3 - 9x^2 + 9x^3\right) \][/tex]
1. Combine like terms inside the parentheses:
- First, group the x² and x³ terms together:
- The x² terms: [tex]\(7x^2 - 9x^2 = -2x^2\)[/tex]
- The x³ terms: [tex]\(-7x^3 + 9x^3 = 2x^3\)[/tex]
So, the expression inside the parentheses simplifies to:
[tex]\[ 2x^3 - 2x^2 \][/tex]
2. Distribute [tex]\(-9\)[/tex] across the simplified expression:
Now we want to multiply each term inside the parentheses by [tex]\(-9\)[/tex]:
[tex]\[
-9(2x^3 - 2x^2) = -9 \cdot 2x^3 + (-9) \cdot (-2x^2)
\][/tex]
- Calculate each term:
- [tex]\(-9 \cdot 2x^3 = -18x^3\)[/tex]
- [tex]\(-9 \cdot (-2x^2) = 18x^2\)[/tex]
3. Combine the results:
The expression becomes:
[tex]\[ -18x^3 + 18x^2 \][/tex]
Thus, the simplified form of the expression is [tex]\(-18x^3 + 18x^2\)[/tex], which matches option B. Therefore, the correct answer is:
B [tex]$-18x^3 + 18x^2$[/tex]
We start with the expression:
[tex]\[ -9\left(7x^2 - 7x^3 - 9x^2 + 9x^3\right) \][/tex]
1. Combine like terms inside the parentheses:
- First, group the x² and x³ terms together:
- The x² terms: [tex]\(7x^2 - 9x^2 = -2x^2\)[/tex]
- The x³ terms: [tex]\(-7x^3 + 9x^3 = 2x^3\)[/tex]
So, the expression inside the parentheses simplifies to:
[tex]\[ 2x^3 - 2x^2 \][/tex]
2. Distribute [tex]\(-9\)[/tex] across the simplified expression:
Now we want to multiply each term inside the parentheses by [tex]\(-9\)[/tex]:
[tex]\[
-9(2x^3 - 2x^2) = -9 \cdot 2x^3 + (-9) \cdot (-2x^2)
\][/tex]
- Calculate each term:
- [tex]\(-9 \cdot 2x^3 = -18x^3\)[/tex]
- [tex]\(-9 \cdot (-2x^2) = 18x^2\)[/tex]
3. Combine the results:
The expression becomes:
[tex]\[ -18x^3 + 18x^2 \][/tex]
Thus, the simplified form of the expression is [tex]\(-18x^3 + 18x^2\)[/tex], which matches option B. Therefore, the correct answer is:
B [tex]$-18x^3 + 18x^2$[/tex]
