Final answer:
To find the product of (4x^2 - 2)(6x^2 + 8x - 5), use the distributive property to multiply each term of the first polynomial by each term of the second polynomial. Then, combine the like terms to get the final product.
Step-by-step explanation:
To find the product of (4x^2 - 2)(6x^2 + 8x - 5), we can use the distributive property. We multiply each term in the first polynomial by each term in the second polynomial and add the resulting terms. Here's how:
Step 1: Multiply 4x^2 by each term in the second polynomial: 4x^2 * 6x^2 = 24x^4, 4x^2 * 8x = 32x^3, and 4x^2 * -5 = -20x^2.
Step 2: Multiply -2 by each term in the second polynomial: -2 * 6x^2 = -12x^2, -2 * 8x = -16x, and -2 * -5 = 10.
Step 3: Combine the like terms obtained in steps 1 and 2: 24x^4 + 32x^3 - 20x^2 - 12x^2 - 16x + 10.
The product is 24x^4 + 32x^3 - 32x^2 - 16x + 10.