Question

1. (4x⁵ + x³ - 7x² + 2)(3x - 1)

Explanation:

Step1: Distribute $3x$ to each term

$3x \cdot 4x^5 + 3x \cdot x^3 - 3x \cdot 7x^2 + 3x \cdot 2$
$=12x^6 + 3x^4 - 21x^3 + 6x$

Step2: Distribute $-1$ to each term

$-1 \cdot 4x^5 -1 \cdot x^3 +1 \cdot 7x^2 -1 \cdot 2$
$=-4x^5 -x^3 +7x^2 -2$

Step3: Combine all terms

$12x^6 + 3x^4 - 21x^3 + 6x -4x^5 -x^3 +7x^2 -2$

Step4: Combine like terms

$12x^6 -4x^5 +3x^4 +(-21x^3 -x^3)+7x^2 +6x -2$
$=12x^6 -4x^5 +3x^4 -22x^3 +7x^2 +6x -2$

Answer:

$12x^6 -4x^5 +3x^4 -22x^3 +7x^2 +6x -2$