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Answer :
To find the product of the given expression [tex]\((4x)(-3x^8)(-7x^3)\)[/tex], we need to multiply both the coefficients and the powers of [tex]\(x\)[/tex] separately.
Step 1: Multiply the coefficients
- The coefficients are 4, -3, and -7.
- First, multiply 4 and -3:
[tex]\[
4 \times (-3) = -12
\][/tex]
- Next, multiply the result by -7:
[tex]\[
-12 \times (-7) = 84
\][/tex]
Step 2: Multiply the powers of [tex]\(x\)[/tex]
- We add the exponents of [tex]\(x\)[/tex] from each term:
- First term: [tex]\(x^1\)[/tex] (since [tex]\(4x\)[/tex] can be written as [tex]\(4x^1\)[/tex])
- Second term: [tex]\(x^8\)[/tex]
- Third term: [tex]\(x^3\)[/tex]
- Add the exponents:
[tex]\[
1 + 8 + 3 = 12
\][/tex]
Step 3: Combine the results
- The resulting product of the expression is:
[tex]\[
84x^{12}
\][/tex]
So, the correct product is [tex]\(84x^{12}\)[/tex]. The answer is [tex]\((84x^{12})\)[/tex], which corresponds to the option [tex]\(84 x^{12}\)[/tex].
Step 1: Multiply the coefficients
- The coefficients are 4, -3, and -7.
- First, multiply 4 and -3:
[tex]\[
4 \times (-3) = -12
\][/tex]
- Next, multiply the result by -7:
[tex]\[
-12 \times (-7) = 84
\][/tex]
Step 2: Multiply the powers of [tex]\(x\)[/tex]
- We add the exponents of [tex]\(x\)[/tex] from each term:
- First term: [tex]\(x^1\)[/tex] (since [tex]\(4x\)[/tex] can be written as [tex]\(4x^1\)[/tex])
- Second term: [tex]\(x^8\)[/tex]
- Third term: [tex]\(x^3\)[/tex]
- Add the exponents:
[tex]\[
1 + 8 + 3 = 12
\][/tex]
Step 3: Combine the results
- The resulting product of the expression is:
[tex]\[
84x^{12}
\][/tex]
So, the correct product is [tex]\(84x^{12}\)[/tex]. The answer is [tex]\((84x^{12})\)[/tex], which corresponds to the option [tex]\(84 x^{12}\)[/tex].
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