Question

How do I solve this? Please show work, thank you.

Answer 1

√(7·x)·(√x - 7·√7)

= √(7·x)·√x - √(7·x)·7·√7

= √7·√x·√x - √7·√x·7·√7

= √7·x - 49·√x

= x·√7 - 49·√x

So answer a is correct.

Answer 2

a x sqrt(7) - 49sqrt(x)

Explanation:

sqrt(7x) [ sqrt(x) - 7sqrt(7)]

Distribute

sqrt(7x) *sqrt(x) - sqrt(7x)*7sqrt(7)

We know that sqrt(a) sqrt(b)= sqrt(ab)

sqrt(7x^2) - 7sqrt(7^2 *x)

Now lets separate out the perfect squares

sqrt(7) *sqrt(x^2) - 7sqrt(7^2)*sqrt(x)

x sqrt(7) - 7*7sqrt(x)

x sqrt(7) - 49sqrt(x)