Answer :
Sure, let's simplify the expression step by step.
We have the expression: [tex]\(-4x^2(3x - 7)\)[/tex].
1. Distribute [tex]\(-4x^2\)[/tex] across the terms inside the parentheses:
- For the first term: [tex]\(-4x^2 \times 3x\)[/tex]
- Multiply the coefficients: [tex]\(-4 \times 3 = -12\)[/tex].
- Combine the powers of [tex]\(x\)[/tex]: [tex]\(x^2 \times x = x^{2+1} = x^3\)[/tex].
- So, the first term becomes [tex]\(-12x^3\)[/tex].
- For the second term: [tex]\(-4x^2 \times -7\)[/tex]
- Multiply the coefficients: [tex]\(-4 \times -7 = 28\)[/tex].
- The power of [tex]\(x\)[/tex] remains the same: [tex]\(x^2\)[/tex].
- So, the second term becomes [tex]\(28x^2\)[/tex].
2. Combine the terms:
The simplified expression is [tex]\(-12x^3 + 28x^2\)[/tex].
Therefore, the correct answer is B. [tex]\(-12x^3 + 28x^2\)[/tex].
We have the expression: [tex]\(-4x^2(3x - 7)\)[/tex].
1. Distribute [tex]\(-4x^2\)[/tex] across the terms inside the parentheses:
- For the first term: [tex]\(-4x^2 \times 3x\)[/tex]
- Multiply the coefficients: [tex]\(-4 \times 3 = -12\)[/tex].
- Combine the powers of [tex]\(x\)[/tex]: [tex]\(x^2 \times x = x^{2+1} = x^3\)[/tex].
- So, the first term becomes [tex]\(-12x^3\)[/tex].
- For the second term: [tex]\(-4x^2 \times -7\)[/tex]
- Multiply the coefficients: [tex]\(-4 \times -7 = 28\)[/tex].
- The power of [tex]\(x\)[/tex] remains the same: [tex]\(x^2\)[/tex].
- So, the second term becomes [tex]\(28x^2\)[/tex].
2. Combine the terms:
The simplified expression is [tex]\(-12x^3 + 28x^2\)[/tex].
Therefore, the correct answer is B. [tex]\(-12x^3 + 28x^2\)[/tex].
