Answer :
To simplify the expression [tex]\(-4x^2(3x - 7)\)[/tex], you need to apply the distributive property. This property states that you multiply the term outside the parentheses by each term inside the parentheses. Let's break it down step-by-step:
1. Distribute [tex]\(-4x^2\)[/tex] to [tex]\(3x\)[/tex]:
- Multiply the coefficients: [tex]\(-4 \times 3 = -12\)[/tex].
- Add the exponents of [tex]\(x\)[/tex]: [tex]\(x^2 \times x^1 = x^{2+1} = x^3\)[/tex].
- This gives us: [tex]\(-12x^3\)[/tex].
2. Distribute [tex]\(-4x^2\)[/tex] to [tex]\(-7\)[/tex]:
- Multiply the coefficients: [tex]\(-4 \times -7 = 28\)[/tex].
- The variable [tex]\(x\)[/tex] stays the same: [tex]\(x^2\)[/tex].
- This results in: [tex]\(28x^2\)[/tex].
3. Combine the terms:
- When you put both terms together, the expression simplifies to: [tex]\(-12x^3 + 28x^2\)[/tex].
The correct simplified expression is [tex]\(-12x^3 + 28x^2\)[/tex], which corresponds to option D: [tex]\(-12x^3 + 28x^2\)[/tex].
1. Distribute [tex]\(-4x^2\)[/tex] to [tex]\(3x\)[/tex]:
- Multiply the coefficients: [tex]\(-4 \times 3 = -12\)[/tex].
- Add the exponents of [tex]\(x\)[/tex]: [tex]\(x^2 \times x^1 = x^{2+1} = x^3\)[/tex].
- This gives us: [tex]\(-12x^3\)[/tex].
2. Distribute [tex]\(-4x^2\)[/tex] to [tex]\(-7\)[/tex]:
- Multiply the coefficients: [tex]\(-4 \times -7 = 28\)[/tex].
- The variable [tex]\(x\)[/tex] stays the same: [tex]\(x^2\)[/tex].
- This results in: [tex]\(28x^2\)[/tex].
3. Combine the terms:
- When you put both terms together, the expression simplifies to: [tex]\(-12x^3 + 28x^2\)[/tex].
The correct simplified expression is [tex]\(-12x^3 + 28x^2\)[/tex], which corresponds to option D: [tex]\(-12x^3 + 28x^2\)[/tex].
