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Answer :
To simplify the expression [tex]\(-4x^2(3x-7)\)[/tex], we'll use the distributive property. This property lets us multiply each term inside the parentheses by the term outside the parentheses.
1. Distribute [tex]\(-4x^2\)[/tex] to [tex]\(3x\)[/tex]:
- Multiply the coefficients: [tex]\(-4 \times 3 = -12\)[/tex].
- Multiply the variables: [tex]\(x^2 \times x = x^{2+1} = x^3\)[/tex].
- So, the result is [tex]\(-12x^3\)[/tex].
2. Distribute [tex]\(-4x^2\)[/tex] to [tex]\(-7\)[/tex]:
- Multiply the coefficients: [tex]\(-4 \times -7 = 28\)[/tex].
- Since there is no [tex]\(x\)[/tex] term with [tex]\(-7\)[/tex], just carry over [tex]\(x^2\)[/tex].
- So, the result is [tex]\(28x^2\)[/tex].
3. Combine the results:
- You get [tex]\(-12x^3 + 28x^2\)[/tex].
Therefore, the simplified expression is [tex]\(-12x^3 + 28x^2\)[/tex].
Looking at the given options, the correct one is:
A. [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].
- Multiply the variables: [tex]\(x^2 \times x = x^{2+1} = x^3\)[/tex].
- So, the result is [tex]\(-12x^3\)[/tex].
2. Distribute [tex]\(-4x^2\)[/tex] to [tex]\(-7\)[/tex]:
- Multiply the coefficients: [tex]\(-4 \times -7 = 28\)[/tex].
- Since there is no [tex]\(x\)[/tex] term with [tex]\(-7\)[/tex], just carry over [tex]\(x^2\)[/tex].
- So, the result is [tex]\(28x^2\)[/tex].
3. Combine the results:
- You get [tex]\(-12x^3 + 28x^2\)[/tex].
Therefore, the simplified expression is [tex]\(-12x^3 + 28x^2\)[/tex].
Looking at the given options, the correct one is:
A. [tex]\(-12x^3 + 28x^2\)[/tex]
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