Question

What is the following simplified product? Assume x greater-than-or-equal-to 0

(StartRoot 6 x squared EndRoot + 4 StartRoot 8 x cubed EndRoot) (StartRoot 9 x EndRoot minus x StartRoot 5 x Superscript 5 Baseline)

A. 3 x StartRoot 6 x EndRoot + x Superscript 4 Baseline StartRoot 30 x EndRoot + 24 x squared + 8 x Superscript 5 Baseline StartRoot 10 x EndRoot
B. 3 x StartRoot 6 x EndRoot + x Superscript 4 Baseline StartRoot 30 x EndRoot + 24 x squared StartRoot 2 EndRoot + 8 x Superscript 5 Baseline StartRoot 10 EndRoot
C. 3 x StartRoot 6 x EndRoot minus x Superscript 4 Baseline StartRoot 30 x EndRoot + 24 x squared StartRoot 2 EndRoot minus 8 x Superscript 5 Baseline StartRoot 10 EndRoot
D. 3 x StartRoot 6 x EndRoot minus x Superscript 4 Baseline StartRoot 30 x EndRoot + 24 x squared StartRoot 2 x EndRoot minus 8 x Superscript 5 Baseline StartRoot 10 x EndRoot

Answer 1

c

Explanation:

Answer 2

Option C is correct.

Explanation:

We have to simplify the product of

(StartRoot 6 x squared EndRoot + 4 StartRoot 8 x cubed EndRoot) (StartRoot 9 x EndRoot minus x StartRoot 5 x Superscript 5 Baseline)

=
`(\sqrt{6x^(2)} + 4\sqrt{8x^(3)})(√(9x) - x\sqrt{5x^(5)})`

=
`(\sqrt{6x^(2)} + \sqrt{128x^(3)})(√(9x) - \sqrt{5x^(7)})`

=
`\sqrt{54x^(3)} - \sqrt{30x^(9)} + \sqrt{1152x^(4)} - \sqrt{640x^(10)}`

=
`3x√(6x) - x^(4)√(30x) + 24x^(2)√(2) - 8x^(5)√(10)`

= 3 x StartRoot 6 x EndRoot minus x Superscript 4 Baseline StartRoot 30 x EndRoot + 24 x squared StartRoot 2 EndRoot minus 8 x Superscript 5 Baseline StartRoot 10 EndRoot

Therefore, option C is correct. (Answer)