Answered

At Westonci.ca, we connect you with experts who provide detailed answers to your most pressing questions. Start exploring now! Join our Q&A platform to connect with experts dedicated to providing precise answers to your questions in different areas. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.

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)

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
semsee45

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.

We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.