Answer :
To simplify the expression [tex]\(-4x^2(3x-7)\)[/tex], we can use the distributive property. Here's a step-by-step breakdown of the process:
1. Apply the Distributive Property:
The distributive property tells us that [tex]\(a(b + c) = ab + ac\)[/tex]. In this case, we have:
[tex]\(-4x^2(3x - 7)\)[/tex].
2. Multiply Each Term Inside the Parentheses by [tex]\(-4x^2\)[/tex]:
- Multiply [tex]\(-4x^2\)[/tex] by [tex]\(3x\)[/tex]:
[tex]\[
-4x^2 \times 3x = -12x^3
\][/tex]
- Multiply [tex]\(-4x^2\)[/tex] by [tex]\(-7\)[/tex]:
[tex]\[
-4x^2 \times -7 = 28x^2
\][/tex]
3. Combine the Resulting Terms:
So, the expression simplified is:
[tex]\[
-12x^3 + 28x^2
\][/tex]
Therefore, the correct answer is A. [tex]\(-12x^3 + 28x^2\)[/tex].
1. Apply the Distributive Property:
The distributive property tells us that [tex]\(a(b + c) = ab + ac\)[/tex]. In this case, we have:
[tex]\(-4x^2(3x - 7)\)[/tex].
2. Multiply Each Term Inside the Parentheses by [tex]\(-4x^2\)[/tex]:
- Multiply [tex]\(-4x^2\)[/tex] by [tex]\(3x\)[/tex]:
[tex]\[
-4x^2 \times 3x = -12x^3
\][/tex]
- Multiply [tex]\(-4x^2\)[/tex] by [tex]\(-7\)[/tex]:
[tex]\[
-4x^2 \times -7 = 28x^2
\][/tex]
3. Combine the Resulting Terms:
So, the expression simplified is:
[tex]\[
-12x^3 + 28x^2
\][/tex]
Therefore, the correct answer is A. [tex]\(-12x^3 + 28x^2\)[/tex].
