Answer :
To simplify the expression [tex]\(-4x^2(3x - 7)\)[/tex], we can apply the distributive property. This property allows us to multiply each term inside the parentheses by the term outside the parentheses.
Let's go through the steps:
1. Multiply [tex]\(-4x^2\)[/tex] by the first term in the parentheses: [tex]\(3x\)[/tex].
[tex]\[
-4x^2 \times 3x = (-4 \times 3) \times (x^2 \times x) = -12x^3
\][/tex]
2. Multiply [tex]\(-4x^2\)[/tex] by the second term in the parentheses: [tex]\(-7\)[/tex].
[tex]\[
-4x^2 \times (-7) = (-4 \times -7) \times x^2 = 28x^2
\][/tex]
3. Combine the results from both multiplications.
The expression simplifies to:
[tex]\[
-12x^3 + 28x^2
\][/tex]
So, the simplified expression is [tex]\(-12x^3 + 28x^2\)[/tex].
Therefore, the correct answer is option A: [tex]\(-12x^3 + 28x^2\)[/tex].
Let's go through the steps:
1. Multiply [tex]\(-4x^2\)[/tex] by the first term in the parentheses: [tex]\(3x\)[/tex].
[tex]\[
-4x^2 \times 3x = (-4 \times 3) \times (x^2 \times x) = -12x^3
\][/tex]
2. Multiply [tex]\(-4x^2\)[/tex] by the second term in the parentheses: [tex]\(-7\)[/tex].
[tex]\[
-4x^2 \times (-7) = (-4 \times -7) \times x^2 = 28x^2
\][/tex]
3. Combine the results from both multiplications.
The expression simplifies to:
[tex]\[
-12x^3 + 28x^2
\][/tex]
So, the simplified expression is [tex]\(-12x^3 + 28x^2\)[/tex].
Therefore, the correct answer is option A: [tex]\(-12x^3 + 28x^2\)[/tex].
