Answer :
Certainly! Let's simplify the expression [tex]\(-4x^2(3x - 7)\)[/tex] step-by-step.
We will use the distributive property, which states that [tex]\(a(b + c) = ab + ac\)[/tex]. In this case, we distribute [tex]\(-4x^2\)[/tex] to both terms inside the parentheses.
1. Distribute [tex]\(-4x^2\)[/tex] to the first term [tex]\(3x\)[/tex]:
[tex]\[
-4x^2 \cdot 3x = -12x^{3}
\][/tex]
2. Next, distribute [tex]\(-4x^2\)[/tex] to the second term [tex]\(-7\)[/tex]:
[tex]\[
-4x^2 \cdot (-7) = 28x^{2}
\][/tex]
3. Now, combine the results from steps 1 and 2:
[tex]\[
-12x^{3} + 28x^{2}
\][/tex]
Therefore, the simplified expression is [tex]\(-12x^{3} + 28x^{2}\)[/tex].
Looking at the choices given:
- A. [tex]\(-12x^3-28x^2\)[/tex]
- B. [tex]\(-12x^3+28\)[/tex]
- C. [tex]\(-12x^3+28x^2\)[/tex]
- D. [tex]\(-12x^3-28\)[/tex]
The correct answer is C. [tex]\(-12x^3+28x^2\)[/tex].
We will use the distributive property, which states that [tex]\(a(b + c) = ab + ac\)[/tex]. In this case, we distribute [tex]\(-4x^2\)[/tex] to both terms inside the parentheses.
1. Distribute [tex]\(-4x^2\)[/tex] to the first term [tex]\(3x\)[/tex]:
[tex]\[
-4x^2 \cdot 3x = -12x^{3}
\][/tex]
2. Next, distribute [tex]\(-4x^2\)[/tex] to the second term [tex]\(-7\)[/tex]:
[tex]\[
-4x^2 \cdot (-7) = 28x^{2}
\][/tex]
3. Now, combine the results from steps 1 and 2:
[tex]\[
-12x^{3} + 28x^{2}
\][/tex]
Therefore, the simplified expression is [tex]\(-12x^{3} + 28x^{2}\)[/tex].
Looking at the choices given:
- A. [tex]\(-12x^3-28x^2\)[/tex]
- B. [tex]\(-12x^3+28\)[/tex]
- C. [tex]\(-12x^3+28x^2\)[/tex]
- D. [tex]\(-12x^3-28\)[/tex]
The correct answer is C. [tex]\(-12x^3+28x^2\)[/tex].
