Question

What is the following simplified product? Assume

Answer 1

The simplified product is:

`10x^4√(6)+x^3√(30x)-10x^4√(3)-x^3√(15x)`

Explanation:

The expression is given by:

`(√(10x^4)-x√(5x^2))(2√(15x^4)+√(3x^3))`

Now we know that:

`√(x^2)=x\\\\and\\\\√(x^4)=√((x^2)^2)=x^2`

Hence, we get the expression as follows:

`(√(10x^4)-x√(5x^2))(2√(15x^4)+√(3x^3))=(x^2√(10)-x\cdot x√(5))(2x^2√(15)+x√(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√(10)(2x^2√(15)+x√(3x))-x^2√(5)(2x^2√(15)+x√(3x))`

`=2x^4√(10)√(15)+x^3√(10)√(3x)-2x^4√(5)√(15)-x^3√(5)√(3x)`

Now we know that:

`√(a)√(b)=√(ab)`

i.e. we have:

`=2x^4√(150)+x^3√(30x)-2x^4√(75)-x^3√(15x)\\\\=2x^4√(5^2\cdot 6)+x^3√(30x)-2x^4√(5^2\cdot 3)-x^3√(15x)\\\\=10x^4√(6)+x^3√(30x)-10x^4√(3)-x^3√(15x)`

Answer 2

The correct answer option is D.
`10x^4√(6)+x^3√(30x)-10x^4√(3)-x^3√(15x)`.

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√(75x^6)-x√(15x^5) \\\\ =2√(25*6x^8)+x^3√(30x)-2x√(25*3x^6)-x^3√(15x) \\\\ =10x^4√(6)+x^3√(30x)-10x^4√(3)-x^3√(15x)`