The distributed simplified product is [tex]2x\sqrt{10x}-2x\sqrt{5}[/tex]. So, option 4 is correct.
What is distributive property?
The distributive property is given by
a(b + c) = ab + ac or (a + b)c = ac + bc.
This property is used for simplifying large expressions into small ones.
The reverse order we can write as
ab + ac = a(b + c) or ac + bc = (a + b)c.
Calculation:
The given expression is [tex]\sqrt{5x}(\sqrt{8x^2}-2\sqrt{x})[/tex]
On applying distributive property: a(b + c) = ab + ac
[tex]\sqrt{5x}(\sqrt{8x^2}-2\sqrt{x})[/tex] = [tex]\sqrt{5x}(\sqrt{8x^2}) - \sqrt{5x}(2\sqrt{x})[/tex]
Applying multiplication of surds,
(multiplication of surds: [tex]\sqrt{a}\times\sqrt{b}=\sqrt{ab}[/tex])
⇒ [tex]x(\sqrt{5x\times8})-2(\sqrt{5x\times x})[/tex]
⇒ [tex]x\sqrt{40x}-2\sqrt{5x^2}[/tex]
⇒ [tex]2\sqrt{10x}-2x\sqrt{5}[/tex]
Therefore, the simplified product for [tex]\sqrt{5x}(\sqrt{8x^2}-2\sqrt{x})[/tex] is [tex]2x\sqrt{10x}-2x\sqrt{5}[/tex].
Thus, option 4 is correct.
Learn more about the distributive property here:
https://brainly.com/question/2807928
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