Answer :
To find the product of [tex]\((4x)(-3x^8)(-7x^3)\)[/tex], we can follow these steps:
1. Multiply the Coefficients:
- Look at the numerical coefficients in front of each term: 4, -3, and -7.
- Multiply these numbers together:
[tex]\[
4 \times (-3) \times (-7) = 84
\][/tex]
- Multiplying a negative number by another negative number results in a positive number, so the product is positive.
2. Add the Exponents of [tex]\( x \)[/tex]:
- When multiplying terms with the same base, we add the exponents according to the exponent rules.
- The exponents for [tex]\( x \)[/tex] are 1, 8, and 3 (from [tex]\( x^1, x^8, x^3 \)[/tex] respectively).
- Add these exponents together:
[tex]\[
1 + 8 + 3 = 12
\][/tex]
3. Combine the Results:
- Combine the product of the coefficients and the sum of the exponents to form the product of the terms:
[tex]\[
84x^{12}
\][/tex]
Therefore, the product [tex]\((4x)(-3x^8)(-7x^3)\)[/tex] equals [tex]\( 84x^{12} \)[/tex]. Hence, the correct answer is [tex]\( 84x^{12} \)[/tex].
1. Multiply the Coefficients:
- Look at the numerical coefficients in front of each term: 4, -3, and -7.
- Multiply these numbers together:
[tex]\[
4 \times (-3) \times (-7) = 84
\][/tex]
- Multiplying a negative number by another negative number results in a positive number, so the product is positive.
2. Add the Exponents of [tex]\( x \)[/tex]:
- When multiplying terms with the same base, we add the exponents according to the exponent rules.
- The exponents for [tex]\( x \)[/tex] are 1, 8, and 3 (from [tex]\( x^1, x^8, x^3 \)[/tex] respectively).
- Add these exponents together:
[tex]\[
1 + 8 + 3 = 12
\][/tex]
3. Combine the Results:
- Combine the product of the coefficients and the sum of the exponents to form the product of the terms:
[tex]\[
84x^{12}
\][/tex]
Therefore, the product [tex]\((4x)(-3x^8)(-7x^3)\)[/tex] equals [tex]\( 84x^{12} \)[/tex]. Hence, the correct answer is [tex]\( 84x^{12} \)[/tex].
