To multiply two polynomials (2x^2 + 6x - 10) and (x^2 - 2x + 2), we use the distributive property. We multiply each term of the first polynomial by each term of the second polynomial and simplify. The steps are as follows:
Distribute the first term of the first polynomial: 2x^2 * (x^2 - 2x + 2) = 2x^4 - 4x^3 + 4x^2.
Distribute the second term of the first polynomial: 6x * (x^2 - 2x + 2) = 6x^3 - 12x^2 + 12x.
Distribute the third term of the first polynomial: -10 * (x^2 - 2x + 2) = -20x^2 + 20x - 20.
Add the results from steps 1-3: 2x^4 - 4x^3 + 4x^2 + 6x^3 - 12x^2 + 12x - 20x^2 + 20x - 20.
Simplify: 2x^4 + 8x^3 - 20x^2 + 20x + 12x - 20.
The result is: 2x^4 + 8x^3 - 20x^2 + 20x + 12x - 20