Find the product of (x² + 2x - 3)(4x² - 5x + 6).

The problem is based on the concept of multiplication of polynomials.

Answer: The product of (x² + 2x - 3)(4x² - 5x + 6) is 4x⁴ + 3x³ - 16x² + 27x - 18

Let us understand how to multiply polynomials with exponents in detail.

Explanation:

When multiplying polynomials, the coefficient is multiplied with a coefficient, and the variable is multiplied with a variable.

Therefore, (x² + 2x - 3)(4x² - 5x + 6) 

= x²(4x² - 5x + 6) + 2x(4x² - 5x + 6) -3(4x² - 5x + 6) 

= 4x⁴ - 5x³ + 6x² + 8x³ - 10x² + 12x - 12x² + 15x - 18

= 4x⁴ + (8 - 5)x³ + (6 - 10 - 12)x² + (12 + 15)x - 18

= 4x⁴ + 3x³  - 16x² + 27x - 18

Thus, (x² + 2x - 3)(4x² - 5x + 6) is equal to 4x⁴ + 3x³ - 16x² + 27x - 18.