Question

question use the box method to distribute and simplify (6 - 6x)(-5x³ - 6x + 4x² + 4 + 5x⁴). drag and drop the terms to the correct locations of the table. (6 - 6x)(-5x³ - 6x + 4x² + 4 + 5x⁴) rows: columns: answer attempt 1 out of 2 you must answer all questions above in order to submit. show examples

Explanation:

Step1: Set up box (2 rows, 5 cols)

Rows: $6, -6x$; Columns: $5x^4, -5x^3, 4x^2, -6x, 4$

Step2: Calculate each box product

1. $6 \times 5x^4 = 30x^4$
2. $6 \times (-5x^3) = -30x^3$
3. $6 \times 4x^2 = 24x^2$
4. $6 \times (-6x) = -36x$
5. $6 \times 4 = 24$
6. $-6x \times 5x^4 = -30x^5$
7. $-6x \times (-5x^3) = 30x^4$
8. $-6x \times 4x^2 = -24x^3$
9. $-6x \times (-6x) = 36x^2$
10. $-6x \times 4 = -24x$

Step3: Combine like terms

$$\begin{align*} &-30x^5 + (30x^4+30x^4) + (-30x^3-24x^3) + (24x^2+36x^2) + (-36x-24x) + 24\\ &=-30x^5 + 60x^4 - 54x^3 + 60x^2 - 60x + 24 \end{align*}$$

Answer:

$-30x^5 + 60x^4 - 54x^3 + 60x^2 - 60x + 24$

Box setup summary (rows × columns):

	$5x^4$	$-5x^3$	$4x^2$	$-6x$	$4$
$-6x$	$-30x^5$	$30x^4$	$-24x^3$	$36x^2$	$-24x$