Question

1. (2x² - 5x + 3)(9x² + 3x - 5)

Explanation:

Step1: Distribute first polynomial terms

Multiply each term in $2x^2-5x+3$ by the second polynomial:
$2x^2(9x^2+3x-5) -5x(9x^2+3x-5) +3(9x^2+3x-5)$

Step2: Expand each product

Calculate each distributed term:
$18x^4 + 6x^3 -10x^2 -45x^3 -15x^2 +25x +27x^2 +9x -15$

Step3: Combine like terms

Group and add/subtract identical degree terms:
$18x^4 + (6x^3-45x^3) + (-10x^2-15x^2+27x^2) + (25x+9x) -15$
$18x^4 -39x^3 +2x^2 +34x -15$

Answer:

$18x^4 - 39x^3 + 2x^2 + 34x - 15$