Answer :
To solve the problem and find the product of the expression [tex]\((4x)(-3x^8)(-7x^3)\)[/tex], let's break it down step by step:
1. Multiply the numbers:
- Look at the coefficients: 4, -3, and -7.
- Multiply them together:
[tex]\[
4 \times (-3) \times (-7) = 84
\][/tex]
- Notice that multiplying two negative numbers (-3 and -7) results in a positive product.
2. Combine the powers of [tex]\( x \)[/tex]:
- Each term has an exponent on [tex]\( x \)[/tex], which are: [tex]\( x^1 \)[/tex], [tex]\( x^8 \)[/tex], and [tex]\( x^3 \)[/tex].
- Add the exponents together:
[tex]\[
1 + 8 + 3 = 12
\][/tex]
3. Put it all together:
- The product of the coefficients is 84.
- The sum of the exponents for [tex]\( x \)[/tex] is 12, which means the result will have [tex]\( x^{12}\)[/tex].
Therefore, the product of the expression [tex]\((4x)(-3x^8)(-7x^3)\)[/tex] is:
[tex]\[ 84x^{12} \][/tex]
So, the correct answer from the options provided is [tex]\( 84x^{12} \)[/tex].
1. Multiply the numbers:
- Look at the coefficients: 4, -3, and -7.
- Multiply them together:
[tex]\[
4 \times (-3) \times (-7) = 84
\][/tex]
- Notice that multiplying two negative numbers (-3 and -7) results in a positive product.
2. Combine the powers of [tex]\( x \)[/tex]:
- Each term has an exponent on [tex]\( x \)[/tex], which are: [tex]\( x^1 \)[/tex], [tex]\( x^8 \)[/tex], and [tex]\( x^3 \)[/tex].
- Add the exponents together:
[tex]\[
1 + 8 + 3 = 12
\][/tex]
3. Put it all together:
- The product of the coefficients is 84.
- The sum of the exponents for [tex]\( x \)[/tex] is 12, which means the result will have [tex]\( x^{12}\)[/tex].
Therefore, the product of the expression [tex]\((4x)(-3x^8)(-7x^3)\)[/tex] is:
[tex]\[ 84x^{12} \][/tex]
So, the correct answer from the options provided is [tex]\( 84x^{12} \)[/tex].
