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Sagot :
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:
Given polynomials
- [tex]2ab+b[/tex]
- [tex]a^2-b^2[/tex]
The product of the given polynomials:
[tex]\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}[/tex]
The product of the given polynomials multiplied by [tex](2a+b)[/tex]:
[tex]\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}[/tex]
Therefore, the resulting polynomial has 8 terms.
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