Answer :
To simplify the expression [tex]\(-4x^2(3x - 7)\)[/tex], we can use the distributive property. Here are the steps:
1. Distribute [tex]\(-4x^2\)[/tex] over both terms inside the parentheses [tex]\((3x - 7)\)[/tex].
[tex]\[ -4x^2 \cdot 3x \][/tex]
[tex]\[ -4x^2 \cdot (-7) \][/tex]
Let's handle these one by one.
2. Multiply [tex]\(-4x^2\)[/tex] by [tex]\(3x\)[/tex]:
[tex]\[ -4x^2 \cdot 3x = (-4 \cdot 3) \cdot (x^2 \cdot x) = -12x^3 \][/tex]
3. Multiply [tex]\(-4x^2\)[/tex] by [tex]\(-7\)[/tex]:
[tex]\[ -4x^2 \cdot (-7) = -4 \cdot (-7) \cdot x^2 = 28x^2 \][/tex]
4. Combine the results:
[tex]\[ -4x^2(3x - 7) = -12x^3 + 28x^2 \][/tex]
So, the simplified expression is [tex]\(-12x^3 + 28x^2\)[/tex].
The correct answer is:
[tex]\[ \boxed{D. -12x^3 + 28x^2} \][/tex]
1. Distribute [tex]\(-4x^2\)[/tex] over both terms inside the parentheses [tex]\((3x - 7)\)[/tex].
[tex]\[ -4x^2 \cdot 3x \][/tex]
[tex]\[ -4x^2 \cdot (-7) \][/tex]
Let's handle these one by one.
2. Multiply [tex]\(-4x^2\)[/tex] by [tex]\(3x\)[/tex]:
[tex]\[ -4x^2 \cdot 3x = (-4 \cdot 3) \cdot (x^2 \cdot x) = -12x^3 \][/tex]
3. Multiply [tex]\(-4x^2\)[/tex] by [tex]\(-7\)[/tex]:
[tex]\[ -4x^2 \cdot (-7) = -4 \cdot (-7) \cdot x^2 = 28x^2 \][/tex]
4. Combine the results:
[tex]\[ -4x^2(3x - 7) = -12x^3 + 28x^2 \][/tex]
So, the simplified expression is [tex]\(-12x^3 + 28x^2\)[/tex].
The correct answer is:
[tex]\[ \boxed{D. -12x^3 + 28x^2} \][/tex]
