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Answer: This is your answer (:      12a^4b^3−30a^5b−4a^2b^4+16a^3b^2−2ab^3

Step-by-step explanation:

((−6a^3)(b)+2ab^2)(5a^2−2ab^2−b)

=((−6a^3)(b)+2ab^2)(5a^2+−2ab^2+−b)

=((−6a^3)(b))(5a^2)+((−6a^3)(b))(−2ab^2)+((−6a^3)(b))(−b)+(2ab^2)(5a^2)+(2ab2)(−2ab2)+(2ab2)(−b)

=−30a^5b+12a^4b^3+6a^3b^2+^10a^3b^2−^4a^2b^4−2ab^3

=12a^4b^3−30a^5b−4a^2b^4+^16a^3b^2−2ab^3

Hope this helps!!! (:

lily9211

Answer:

[tex]-30a^5b+12a^4b^3+16a^3b^2-4a^2b^4-2ab^3[/tex]

Step-by-step explanation:

Multiplying polynomials is just like multiplying other numbers using the distributive property.

If you take the parentheses off the binomial (the polynomial on the left) then you can see that you can distribute the -6a^3b to all of the terms on the right and 2ab^2 to all of the terms on the right.

Start by distributing -6a^3b inside the parentheses.

-6a^3b(5a^2 - 2ab^2 - b)

  • -6a^3b * 5a^2 = [tex]-30a^5b[/tex]
  • -6a^3b *-2ab^2 = [tex]12a^4 b^3[/tex]
  • -6a^3b * -b = [tex]6a^3b^2[/tex]

Now distribute 2ab^2 inside the parentheses.

  • 2ab^2 * 5a^2 = [tex]10a^3b^2[/tex]
  • 2ab^2 * -2ab^2 = [tex]-4a^2b^4[/tex]
  • 2ab^2 * -b = [tex]-2ab^3[/tex]

Take all of these answers and add them together (combine like terms).

  • [tex]-30a^5b +12a^4 b^3+6a^3b^2+10a^3b^2-4a^2b^4-2ab^3[/tex]
  • = [tex]-30a^5b+12a^4b^3+16a^3b^2-4a^2b^4-2ab^3[/tex]

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