Answer :
To simplify the expression [tex]\( -4x^2(3x - 7) \)[/tex], we need to distribute [tex]\( -4x^2 \)[/tex] across the terms inside the parentheses. Let's take this one step at a time:
1. Distribute [tex]\( -4x^2 \)[/tex] to the first term in the parentheses:
Multiply [tex]\( -4x^2 \)[/tex] by [tex]\( 3x \)[/tex]:
[tex]\[
(-4x^2) \cdot (3x) = -4 \cdot 3 \cdot x^2 \cdot x = -12x^{2+1} = -12x^3
\][/tex]
2. Distribute [tex]\( -4x^2 \)[/tex] to the second term in the parentheses:
Multiply [tex]\( -4x^2 \)[/tex] by [tex]\(-7\)[/tex]:
[tex]\[
(-4x^2) \cdot (-7) = -4 \cdot (-7) \cdot x^2 = 28x^2
\][/tex]
3. Combine the results:
Putting the terms together, the expression simplifies to:
[tex]\[
-12x^3 + 28x^2
\][/tex]
Therefore, the simplified expression is [tex]\( -12x^3 + 28x^2 \)[/tex].
The correct answer choice is A. [tex]\(-12x^3 - 28x^2\)[/tex].
1. Distribute [tex]\( -4x^2 \)[/tex] to the first term in the parentheses:
Multiply [tex]\( -4x^2 \)[/tex] by [tex]\( 3x \)[/tex]:
[tex]\[
(-4x^2) \cdot (3x) = -4 \cdot 3 \cdot x^2 \cdot x = -12x^{2+1} = -12x^3
\][/tex]
2. Distribute [tex]\( -4x^2 \)[/tex] to the second term in the parentheses:
Multiply [tex]\( -4x^2 \)[/tex] by [tex]\(-7\)[/tex]:
[tex]\[
(-4x^2) \cdot (-7) = -4 \cdot (-7) \cdot x^2 = 28x^2
\][/tex]
3. Combine the results:
Putting the terms together, the expression simplifies to:
[tex]\[
-12x^3 + 28x^2
\][/tex]
Therefore, the simplified expression is [tex]\( -12x^3 + 28x^2 \)[/tex].
The correct answer choice is A. [tex]\(-12x^3 - 28x^2\)[/tex].
