Answer:
[tex]\bold{10x^4\sqrt{6}+x^3\sqrt{30x}-10x^4\sqrt{3}-x^3\sqrt{15x}}[/tex]
Step-by-step explanation:
To find:
Simplified product of:
[tex](\sqrt{10x^4}-x\sqrt{5x^2})(2\sqrt{15x^4}+\sqrt{3x^3})[/tex]
Solution:
First of all, let us have a look at some of the formula:
1. [tex](a+b) (c+d) = ac+bc+ad+bd[/tex]
2. [tex]a^b\times a^c =a^{b+c }[/tex]
3. [tex]\sqrt{a^{2b}} = \sqrt{a^b.a^b}=a^b[/tex]
4. [tex]\sqrt a \times \sqrt b = \sqrt{a\times b}[/tex]
Now, let us apply the above formula to solve the given expression.
[tex](\sqrt{10x^4}-x\sqrt{5x^2})(2\sqrt{15x^4}+\sqrt{3x^3})\\\\\Rightarrow(\sqrt{10x^4})(2\sqrt{15x^4})+(\sqrt{10x^4})(\sqrt{3x^3})-(x\sqrt{5x^2})(2\sqrt{15x^4})-(x\sqrt{5x^2})(\sqrt{3x^3})\\\\\Rightarrow2\sqrt{150x^8}+\sqrt{30x^7}-2x\sqrt{75x^6}-x\sqrt{15x^5}\\\\\Rightarrow\bold{10x^4\sqrt{6}+x^3\sqrt{30x}-10x^4\sqrt{3}-x^3\sqrt{15x}}[/tex]
The answer is:
[tex]\bold{10x^4\sqrt{6}+x^3\sqrt{30x}-10x^4\sqrt{3}-x^3\sqrt{15x}}[/tex]
