The simplified product of [tex]2\sqrt{5x^3}(-3\sqrt{10x^2} )[/tex] is [tex]-30x^2\sqrt{2x}[/tex]. Therefore the correct option is b).
Given :
[tex]2\sqrt{5x^3}(-3\sqrt{10x^2} )[/tex]
Solution :
-3 is multiplied by 2 in the first step.
[tex]2\sqrt{5x^3}(-3\sqrt{10x^2} ) = -6(\sqrt{5x^3} \sqrt{10x^2} )[/tex]
The simplification of the result is performed.
[tex]2\sqrt{5x^3}(-3\sqrt{10x^2} ) = -6(\sqrt{5x^3\times10x^2} )[/tex]
Further simplicification by multiplying 5 by 10.
[tex]2\sqrt{5x^3}(-3\sqrt{10x^2} ) = -6(\sqrt{50x^5} )[/tex]
The further simplification is performed.
[tex]2\sqrt{5x^3}(-3\sqrt{10x^2} ) = -30x^2(\sqrt{2x} )[/tex]
The simplified product of [tex]2\sqrt{5x^3}(-3\sqrt{10x^2} )[/tex] is [tex]-30x^2\sqrt{2x}[/tex]. Therefore the correct option is b).
For more inforrmation, refer the link given below
https://brainly.com/question/13911928
