Question

What is the following simplified product? Assume x greater-than-or-equal-to 0 (StartRoot 10 x Superscript 4 Baseline EndRoot minus x StarRoot 5 x squared EndRoot) (2 StartRoot 15 x Superscript 4 Baseline EndRoot + StartRoot 3 x cubed EndRoot) 10 x Superscript 4 Baseline StartRoot 6 EndRoot + x cubed StartRoot 30 x EndRoot minus 10 x Superscript 4 Baseline StartRoot 3 EndRoot + x squared StartRoot 15 x EndRoot 11 x Superscript 4 Baseline StartRoot 6 EndRoot + x cubed StartRoot 30 x EndRoot minus x Superscript 4 Baseline StartRoot 75 EndRoot + x squared StartRoot 15 EndRoot 10 x Superscript 4 Baseline StartRoot 6 EndRoot + x cubed StartRoot 30 x EndRoot minus 10 x Superscript 4 Baseline StartRoot 3 EndRoot minus x squared StartRoot 15 EndRoot 11 x Superscript 4 Baseline StartRoot 6 EndRoot + x cubed StartRoot 30 x EndRoot minus 10 x Superscript 4 Baseline StartRoot 3 EndRoot minus x cubed StartRoot 15 x EndRoot

Answer 1

Its D

Explanation:

Answer 2

`\bold{10x^4√(6)+x^3√(30x)-10x^4√(3)-x^3√(15x)}`

Explanation:

To find:

Simplified product of:

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

Solution:

First of all, let us have a look at some of the formula:

1.
`(a+b) (c+d) = ac+bc+ad+bd`

2.
`a^b* a^c =a^(b+c )`

3.
`\sqrt{a^(2b)} = √(a^b.a^b)=a^b`

4.
`\sqrt a * \sqrt b = √(a* b)`

Now, let us apply the above formula to solve the given expression.

`(√(10x^4)-x√(5x^2))(2√(15x^4)+√(3x^3))\\\\\Rightarrow(√(10x^4))(2√(15x^4))+(√(10x^4))(√(3x^3))-(x√(5x^2))(2√(15x^4))-(x√(5x^2))(√(3x^3))\\\\\Rightarrow2√(150x^8)+√(30x^7)-2x√(75x^6)-x√(15x^5)\\\\\Rightarrow\bold{10x^4√(6)+x^3√(30x)-10x^4√(3)-x^3√(15x)}`

The answer is:

`\bold{10x^4√(6)+x^3√(30x)-10x^4√(3)-x^3√(15x)}`