Question

what value of $n$ makes the statement true?
$6x^{n} \cdot 4x^{2} = 24x^{6}$
$n = 4$
complete
what value of $c$ makes the statement true?
$-2x^{3}(cx^{3} + x^{2}) = -10x^{6} - 2x^{5}$
$c = $
done

Explanation:

Step1: Expand left-hand side

$$\begin{align*} -2x^3(cx^3 + x^2) &= -2x^3 \cdot cx^3 + (-2x^3) \cdot x^2 \\ &= -2c x^{3+3} - 2x^{3+2} \\ &= -2c x^6 - 2x^5 \end{align*}$$

Step2: Equate coefficients of $x^6$

Set $-2c = -10$

Step3: Solve for $c$

$c = \frac{-10}{-2} = 5$

Answer:

$c=5$