Question

What is the following simplified product? Assume

Answer 1

Answer:

The simplified product is:

       $10x^4\sqrt{6}+x^3\sqrt{30x}-10x^4\sqrt{3}-x^3\sqrt{15x}$

Step-by-step explanation:

The expression is given by:

$(\sqrt{10x^4}-x\sqrt{5x^2})(2\sqrt{15x^4}+\sqrt{3x^3})$

Now we know that:

$\sqrt{x^2}=x\\\\and\\\\\sqrt{x^4}=\sqrt{(x^2)^2}=x^2$

Hence, we get the expression as follows:

$(\sqrt{10x^4}-x\sqrt{5x^2})(2\sqrt{15x^4}+\sqrt{3x^3})=(x^2\sqrt{10}-x\cdot x\sqrt{5})(2x^2\sqrt{15}+x\sqrt{3x})$

Now, we will use the property that:

$(a+b)(c+d)=a(c+d)+b(c+d)$

Hence, we have the expression as:

$=x^2\sqrt{10}(2x^2\sqrt{15}+x\sqrt{3x})-x^2\sqrt{5}(2x^2\sqrt{15}+x\sqrt{3x})$

$=2x^4\sqrt{10}\sqrt{15}+x^3\sqrt{10}\sqrt{3x}-2x^4\sqrt{5}\sqrt{15}-x^3\sqrt{5}\sqrt{3x}$

Now we know that:

$\sqrt{a}\sqrt{b}=\sqrt{ab}$

i.e. we have:

$=2x^4\sqrt{150}+x^3\sqrt{30x}-2x^4\sqrt{75}-x^3\sqrt{15x}\\\\=2x^4\sqrt{5^2\cdot 6}+x^3\sqrt{30x}-2x^4\sqrt{5^2\cdot 3}-x^3\sqrt{15x}\\\\=10x^4\sqrt{6}+x^3\sqrt{30x}-10x^4\sqrt{3}-x^3\sqrt{15x}$

Answer 2

Answer:

The correct answer option is D. $10x^4\sqrt{6}+x^3\sqrt{30x}-10x^4\sqrt{3}-x^3\sqrt{15x}$.

Step-by-step explanation:

We are given the following expression:

$\left ( \sqrt { 10 x ^ 4 } -x \sqrt { 5 x ^ 2 } \right ) \left ( 2 \sqrt { 15 x ^ 4 } + \sqrt { 3 x ^ 3 } \right )$

Assuming that $x\geq 0$, we are to find its simplified product.

$\left ( \sqrt { 10 x ^ 4 } -x \sqrt { 5 x ^ 2 } \right ) \left ( 2 \sqrt { 15 x ^ 4 } + \sqrt { 3 x ^ 3 } \right )$

$\\\\ = 2 \sqrt { 150 x ^ 8 } + \sqrt { 3 0 x ^ 7 }-2x\sqrt{75x^6}-x\sqrt{15x^5} \\\\ =2\sqrt{25\times6x^8}+x^3\sqrt{30x}-2x\sqrt{25\times3x^6}-x^3\sqrt{15x} \\\\ =10x^4\sqrt{6}+x^3\sqrt{30x}-10x^4\sqrt{3}-x^3\sqrt{15x}$