Answer :
Sure! Let's simplify the expression [tex]\(-4x^2(3x - 7)\)[/tex] step by step.
1. Distribute the [tex]\(-4x^2\)[/tex]: We need to apply the distributive property, which involves multiplying [tex]\(-4x^2\)[/tex] by each term inside the parentheses.
- Multiply [tex]\(-4x^2\)[/tex] by [tex]\(3x\)[/tex]:
[tex]\[
-4x^2 \times 3x = -12x^{2+1} = -12x^3
\][/tex]
- Multiply [tex]\(-4x^2\)[/tex] by [tex]\(-7\)[/tex]:
[tex]\[
-4x^2 \times (-7) = 28x^2
\][/tex]
2. Combine the results: Add together the terms obtained from the distribution.
[tex]\[
-12x^3 + 28x^2
\][/tex]
Therefore, the simplified expression is [tex]\(-12x^3 + 28x^2\)[/tex].
The correct answer is B. [tex]\(-12x^3 + 28x^2\)[/tex].
1. Distribute the [tex]\(-4x^2\)[/tex]: We need to apply the distributive property, which involves multiplying [tex]\(-4x^2\)[/tex] by each term inside the parentheses.
- Multiply [tex]\(-4x^2\)[/tex] by [tex]\(3x\)[/tex]:
[tex]\[
-4x^2 \times 3x = -12x^{2+1} = -12x^3
\][/tex]
- Multiply [tex]\(-4x^2\)[/tex] by [tex]\(-7\)[/tex]:
[tex]\[
-4x^2 \times (-7) = 28x^2
\][/tex]
2. Combine the results: Add together the terms obtained from the distribution.
[tex]\[
-12x^3 + 28x^2
\][/tex]
Therefore, the simplified expression is [tex]\(-12x^3 + 28x^2\)[/tex].
The correct answer is B. [tex]\(-12x^3 + 28x^2\)[/tex].
