Question

The product of the polynomials (2ab + b) and (2² - b²) is a polynomial with __________ terms. If this product is multiplied by (2a + b), the result is a polynomial with __________ terms.

A. 2; 4
B. 3; 6
C. 4; 8
D. 5; 10

Answer 1

The product of the polynomials (2ab + b) and (2² - b²) results in a polynomial with 3 terms. When multiplied by (2a + b), the result is a polynomial with 6 terms before combining like terms. The answer is option B.

Step-by-step explanation:

The product of the polynomials (2ab + b) and (2² - b²) is a polynomial with 3 terms after applying the distributive property (also known as the FOIL method). The first polynomial has 2 terms, and the second one is a difference of squares, which also has 2 terms. However, after multiplying, some terms may cancel out due to the nature of the difference of squares; hence the product will only have 3 distinct terms.

When this product is further multiplied by (2a + b), it's equivalent to multiplying a trinomial by a binomial. This operation will generate a maximum of 6 terms (3 times 2 terms). Nonetheless, some may combine to reduce the count of distinct terms. However, to answer the question, before combination, there would be 6 terms.

The correct answer is B. 3; 6.