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Answer :
To simplify the expression [tex]\(-4x^2(3x-7)\)[/tex], we'll use the distributive property. This property allows us to multiply each term inside the parenthesis by the term outside.
Let's go through it step-by-step:
1. Multiply [tex]\(-4x^2\)[/tex] by [tex]\(3x\)[/tex]:
- When you multiply the coefficients, [tex]\(-4 \times 3 = -12\)[/tex].
- For the variables, multiplying [tex]\(x^2\)[/tex] by [tex]\(x\)[/tex] gives [tex]\(x^{2+1} = x^3\)[/tex].
- So, [tex]\(-4x^2 \times 3x = -12x^3\)[/tex].
2. Multiply [tex]\(-4x^2\)[/tex] by [tex]\(-7\)[/tex]:
- Multiply the coefficients, [tex]\(-4 \times -7 = 28\)[/tex].
- The variable part remains the same, [tex]\(x^2\)[/tex], because there is no [tex]\(x\)[/tex] in the other term to multiply with.
- So, [tex]\(-4x^2 \times -7 = 28x^2\)[/tex].
Now, put both results together:
[tex]\(-12x^3 + 28x^2\)[/tex]
Therefore, the simplified expression is [tex]\(-12x^3 + 28x^2\)[/tex], which corresponds to choice B.
Let's go through it step-by-step:
1. Multiply [tex]\(-4x^2\)[/tex] by [tex]\(3x\)[/tex]:
- When you multiply the coefficients, [tex]\(-4 \times 3 = -12\)[/tex].
- For the variables, multiplying [tex]\(x^2\)[/tex] by [tex]\(x\)[/tex] gives [tex]\(x^{2+1} = x^3\)[/tex].
- So, [tex]\(-4x^2 \times 3x = -12x^3\)[/tex].
2. Multiply [tex]\(-4x^2\)[/tex] by [tex]\(-7\)[/tex]:
- Multiply the coefficients, [tex]\(-4 \times -7 = 28\)[/tex].
- The variable part remains the same, [tex]\(x^2\)[/tex], because there is no [tex]\(x\)[/tex] in the other term to multiply with.
- So, [tex]\(-4x^2 \times -7 = 28x^2\)[/tex].
Now, put both results together:
[tex]\(-12x^3 + 28x^2\)[/tex]
Therefore, the simplified expression is [tex]\(-12x^3 + 28x^2\)[/tex], which corresponds to choice B.
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