Question

Select the correct answer from each drop-down menu. The product of the polynomials (2ab + b) and (a2 – b2) is . If this product is multiplied by (2a + b), the result is a polynomial with terms. The choices for the terms are (7,8,9,10)

Answer 1

First product

• (2ab+b)(a²-b²)
• a²(2ab+b)-b²(2ab+b)
• 2a³b+a²b-2ab³-b³

Second and final product

• (2a³b)+a²b-2ab³-b³)(2a+b)
• 2a(2a³b+a²b-2ab³-b³)+b(2a³b)+a²b-2ab³-b³)
• 4a⁴b+2a³b-4a²b³-2ab³+2a³b²+a²b²-2ab⁴-b⁴

Answer 2

Given polynomials

• 
  `2ab+b`
• 
  `a^2-b^2`

The product of the given polynomials:

`\begin{aligned}(2ab+b)(a^2-b^2) & = 2ab(a^2-b^2)+b(a^2-b^2)\\& = 2a^3b-2ab^3+a^2b-b^3\end{aligned}`

The product of the given polynomials multiplied by
`(2a+b)`:

`\begin{aligned}(2a+b)(2a^3b-2ab^3+a^2b-b^3) & = 2a(2a^3b-2ab^3+a^2b-b^3)+b(2a^3b-2ab^3+a^2b-b^3)\\& = 4a^4b-4a^2b^3+2a^3b-2ab^3+2a^3b^2-2ab^4+a^2b^2-b^4\\& = 4a^4b+2a^3b^2-4a^2b^3-2ab^4+2a^3b+a^2b^2-2ab^3-b^4\end{aligned}`

Therefore, the resulting polynomial has 8 terms.