Answer :
To simplify the expression [tex]\(-4x^2(3x - 7)\)[/tex], we can use the distributive property. Here’s a step-by-step process:
1. Apply the Distributive Property: This property states that [tex]\(a(b + c) = ab + ac\)[/tex]. We will apply it to [tex]\(-4x^2\)[/tex] and the terms inside the parentheses.
2. Multiply [tex]\(-4x^2\)[/tex] by each term inside the parentheses:
- First, multiply [tex]\(-4x^2\)[/tex] by [tex]\(3x\)[/tex]:
[tex]\[
-4x^2 \times 3x = -12x^3
\][/tex]
- Next, multiply [tex]\(-4x^2\)[/tex] by [tex]\(-7\)[/tex]:
[tex]\[
-4x^2 \times -7 = +28x^2
\][/tex]
3. Combine the results: Now that you have both terms resulting from the multiplication, combine them to get the simplified expression:
[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. Apply the Distributive Property: This property states that [tex]\(a(b + c) = ab + ac\)[/tex]. We will apply it to [tex]\(-4x^2\)[/tex] and the terms inside the parentheses.
2. Multiply [tex]\(-4x^2\)[/tex] by each term inside the parentheses:
- First, multiply [tex]\(-4x^2\)[/tex] by [tex]\(3x\)[/tex]:
[tex]\[
-4x^2 \times 3x = -12x^3
\][/tex]
- Next, multiply [tex]\(-4x^2\)[/tex] by [tex]\(-7\)[/tex]:
[tex]\[
-4x^2 \times -7 = +28x^2
\][/tex]
3. Combine the results: Now that you have both terms resulting from the multiplication, combine them to get the simplified expression:
[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]
