Answer :
Let's find the product of the expression [tex]\((4x)(-3x^8)(-7x^3)\)[/tex].
1. Multiply the Coefficients:
First, we need to multiply the coefficients of the terms together:
[tex]\[
4 \times (-3) \times (-7) = 4 \times 21 = 84
\][/tex]
Multiplying [tex]\(-3\)[/tex] and [tex]\(-7\)[/tex] gives us a positive 21, and then multiplying by 4 results in 84.
2. Multiply the Variables:
Next, we need to multiply the variables with their exponents. When multiplying variables with the same base, we add the exponents. The expression is:
[tex]\[
x^1 \times x^8 \times x^3
\][/tex]
Add the exponents:
[tex]\[
1 + 8 + 3 = 12
\][/tex]
3. Combine the Parts:
Now, combine the calculated coefficient and the exponent:
[tex]\[
84x^{12}
\][/tex]
Therefore, the product of [tex]\((4x)(-3x^8)(-7x^3)\)[/tex] is [tex]\(84x^{12}\)[/tex].
So, the correct answer is:
[tex]\[ 84x^{12} \][/tex]
1. Multiply the Coefficients:
First, we need to multiply the coefficients of the terms together:
[tex]\[
4 \times (-3) \times (-7) = 4 \times 21 = 84
\][/tex]
Multiplying [tex]\(-3\)[/tex] and [tex]\(-7\)[/tex] gives us a positive 21, and then multiplying by 4 results in 84.
2. Multiply the Variables:
Next, we need to multiply the variables with their exponents. When multiplying variables with the same base, we add the exponents. The expression is:
[tex]\[
x^1 \times x^8 \times x^3
\][/tex]
Add the exponents:
[tex]\[
1 + 8 + 3 = 12
\][/tex]
3. Combine the Parts:
Now, combine the calculated coefficient and the exponent:
[tex]\[
84x^{12}
\][/tex]
Therefore, the product of [tex]\((4x)(-3x^8)(-7x^3)\)[/tex] is [tex]\(84x^{12}\)[/tex].
So, the correct answer is:
[tex]\[ 84x^{12} \][/tex]
