Answer :
To simplify the product
[tex]$$
(4x)(-3x^8)(-7x^3),
$$[/tex]
we need to multiply the numerical coefficients and then add the exponents of the variable [tex]$x$[/tex].
Step 1: Multiply the coefficients
The coefficients are [tex]$4$[/tex], [tex]$-3$[/tex], and [tex]$-7$[/tex]. Multiply them as follows:
[tex]$$
4 \times (-3) = -12,
$$[/tex]
[tex]$$
-12 \times (-7) = 84.
$$[/tex]
Step 2: Add the exponents of [tex]$x$[/tex]
The exponents on [tex]$x$[/tex] in the three terms are [tex]$1$[/tex], [tex]$8$[/tex], and [tex]$3$[/tex], respectively (since [tex]$x = x^1$[/tex]). Add these exponents:
[tex]$$
1 + 8 + 3 = 12.
$$[/tex]
Step 3: Write the final product
Combine the product of the coefficients with the variable part:
[tex]$$
84 \times x^{12} = 84x^{12}.
$$[/tex]
Thus, the final answer is:
[tex]$$
84x^{12}.
$$[/tex]
[tex]$$
(4x)(-3x^8)(-7x^3),
$$[/tex]
we need to multiply the numerical coefficients and then add the exponents of the variable [tex]$x$[/tex].
Step 1: Multiply the coefficients
The coefficients are [tex]$4$[/tex], [tex]$-3$[/tex], and [tex]$-7$[/tex]. Multiply them as follows:
[tex]$$
4 \times (-3) = -12,
$$[/tex]
[tex]$$
-12 \times (-7) = 84.
$$[/tex]
Step 2: Add the exponents of [tex]$x$[/tex]
The exponents on [tex]$x$[/tex] in the three terms are [tex]$1$[/tex], [tex]$8$[/tex], and [tex]$3$[/tex], respectively (since [tex]$x = x^1$[/tex]). Add these exponents:
[tex]$$
1 + 8 + 3 = 12.
$$[/tex]
Step 3: Write the final product
Combine the product of the coefficients with the variable part:
[tex]$$
84 \times x^{12} = 84x^{12}.
$$[/tex]
Thus, the final answer is:
[tex]$$
84x^{12}.
$$[/tex]
