Question

rewrite without parentheses.
$-3x^{6}\left(-7x^{3} + 8x^{2} + 4x\
ight)$
simplify your answer as much as possible.

Explanation:

Step1: Distribute $-3x^6$ to each term

Multiply $-3x^6$ by $-7x^3$, $8x^2$, and $4x$ respectively.

$$\begin{align*} -3x^6(-7x^3) + (-3x^6)(8x^2) + (-3x^6)(4x) \end{align*}$$

Step2: Compute each product using exponent rule $x^a \cdot x^b = x^{a+b}$

Calculate coefficients and add exponents of $x$ for each term.

$$\begin{align*} (-3 \times -7)x^{6+3} + (-3 \times 8)x^{6+2} + (-3 \times 4)x^{6+1} \end{align*}$$

Step3: Simplify coefficients and exponents

Simplify each term to get the final expression.

$$\begin{align*} 21x^9 -24x^8 -12x^7 \end{align*}$$

Answer:

$21x^9 - 24x^8 - 12x^7$