Question

What is the following simplified product? Assume x ≥ 0.

(√6x² +4√8x³)(√x-x√√5x5
O3x√6x+x4√30x
+24x² √2x+8x5 √/10x
3x√6x+x4√30x +24x² √√2+8x5/10
3x6x-x√30x+24x²
√2-8x5 10
3x√6x-x√30x +24x² √√2x-8x5 /10x

Answer 1

(c) 3x√(6x) -x⁴√(30x) +24x²√2 -8x⁵√10

Explanation:

You want to simplify the product ...

`(√(6x^2)+4√(8x^3))(√(9x)-x√(5x^5))`

Choices

As with a lot of problems of this type, the correct answer choice can be selected by examining a term or two.

Multiplying the last two terms of the binomials, we get ...

`4√(8x^3)\cdot (-x√(5x^5))=-4x√(40x^8)=-4x√(10(2x^4)^2)=\boxed{-8x^5√(10)}`

This term is only found in choice C.

__

Additional comment

The expression is simplified by making use of the radical relations ...

(√a)(√b) = √(ab)

√(a²b) = a√b

The given expression can be rewritten with squares taken out of the radicals as ...

(x√6 +8x√(2x))·(3√x -x³√(5x))

Then, using FOIL or the distributive property, we have ...

= 3x√(6x) +24x²√2 -x⁴√(30x) -8x⁵√10 . . . . . matches C