Question

What is the value of (sqrt(3) + 3sqrt(27))(2sqrt(3)-sqrt(27))

I know the answer is -30, but I don't know how to solve this one either!

Answer 1

-30

Explanation:

You can work this two ways. One way is to factor √3 from both binomials. We'll show that second. The other way is to multiply it out in the usual way.

Multiply it out

`(√(3)+3√(27))(2√(3)-√(27))\\\\=(√(3))(2√(3))+(√(3))(-√(27))+(3√(27))(2√(3))+(3√(27))(-√(27))\\\\=2√(9)-√(81)+6√(81)-3√(27^2)\\\\=2\cdot 3-9+6\cdot 9-3\cdot 27\\\\=6-9+54-81=-30`

Simplify it first

`(√(3)+3√(27))(2√(3)-√(27))\\\\=(√(3)(1+3√(9)))(√(3)(2-√(9)))\\\\=3(1+3\cdot 3)(2-3)=3(10)(-1)=-30`

To me, the latter method seems easier.