Final answer:
To find the product of the polynomials (2ab + b) and (a^2-b^2), multiply each term in the first polynomial by each term in the second polynomial. If this product is multiplied by (2a + b), the result is a polynomial with 6 terms.
Step-by-step explanation:
To find the product of the polynomials (2ab + b) and (a^2-b^2), we can use the distributive property. Multiply each term in the first polynomial by each term in the second polynomial:
(2ab + b)(a^2-b^2) = 2ab(a^2) + 2ab(-b^2) + b(a^2) - b(b^2)
Simplifying this expression, we get: 2a^3b - 2ab^3 + a^2b - b^3
If we multiply this expression by (2a + b), we can again use the distributive property:
(2a + b)(2a^3b - 2ab^3 + a^2b - b^3) = 4a^4b + 2a^3b^2 + 2a^2b^2 - 2ab^4 + 2a^2b - b^4
The result is a polynomial with 6 terms.