Answer :
Let's simplify the expression step by step:
Given the expression:
[tex]\[ -4 x^2 (3 x - 7) \][/tex]
We need to distribute [tex]\(-4 x^2\)[/tex] to both terms inside the parentheses:
1. First, distribute [tex]\(-4 x^2\)[/tex] to [tex]\(3 x\)[/tex]:
[tex]\[ -4 x^2 \cdot 3 x = -12 x^3 \][/tex]
2. Next, distribute [tex]\(-4 x^2\)[/tex] to [tex]\(-7\)[/tex]:
[tex]\[ -4 x^2 \cdot -7 = 28 x^2 \][/tex]
Now, combine the results of these two distributions:
[tex]\[ -12 x^3 + 28 x^2 \][/tex]
Therefore, the simplified expression is:
[tex]\[ \boxed{-12 x^3 + 28 x^2} \][/tex]
Among the given choices, the correct answer is:
B. [tex]\(-12 x^3 + 28 x^2\)[/tex]
Given the expression:
[tex]\[ -4 x^2 (3 x - 7) \][/tex]
We need to distribute [tex]\(-4 x^2\)[/tex] to both terms inside the parentheses:
1. First, distribute [tex]\(-4 x^2\)[/tex] to [tex]\(3 x\)[/tex]:
[tex]\[ -4 x^2 \cdot 3 x = -12 x^3 \][/tex]
2. Next, distribute [tex]\(-4 x^2\)[/tex] to [tex]\(-7\)[/tex]:
[tex]\[ -4 x^2 \cdot -7 = 28 x^2 \][/tex]
Now, combine the results of these two distributions:
[tex]\[ -12 x^3 + 28 x^2 \][/tex]
Therefore, the simplified expression is:
[tex]\[ \boxed{-12 x^3 + 28 x^2} \][/tex]
Among the given choices, the correct answer is:
B. [tex]\(-12 x^3 + 28 x^2\)[/tex]
