Find the product?

Question

(-2√a - 2√b)(-2√a + 2√b)

What rules apply here? Besides foiling how do you combine the like terms, this is just an example, not sure if it works out!

Answer 1

Multiplying out the brackets:
(-2√a - 2√b)(-2√a + 2√b)=(-2√a*-2√a) + (-2√a*2√b) + (- 2√b*-2√a) + (- 2√b*2√b)
=(4a) + (-4√a√b) + (4√a√b) + (-4b)
= 4a - 4b
= 4(a-b)

If you look at what you started with in the brackets, you have
(x+y)(x-y) which we know just gives x^2 - y^2
So you can straight away tell that the answer will be
(-2√a)^2 - (2√b)^2
Which is 4a-4b

Answer 2

Take, for example, -2√a * -2√a

That is, in effect -2 * √a * -2 * √a or -2 * -2 * √a * √a which is 4a

In this case you don't have to work it all out like that

(a + b)(a - b) is simply (a^2 - b^2)
a = -2√a, b is 2√b

Your answer would be (-2√a * -2√a) - (2√b * 2√b) = 4a - 4b = 4(a - b)

Answer 3

a^1/2 x a ^ 1/2 = a^2/2 = a

Rule is a^m x a^n = a^mn

2a^1/2 x 2 a^1/2 = 4 a
2 a ^ 1/2 x 2 b^ 1/2 = 4 (ab)^1/2 or 4 rad ab

Answer 4

(-2√a - 2√b)(-2√a + 2√b) = .(-)
(2√a + 2√b)(2√a - 2√b) =
(2√a)² -(2√b)² =
4a - 4b = 4(a-b)
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Answer 5

(a-b)(a+b)=a^2-b^2 applies here:

Hence, 4a-4b is the answer

Answer 6

4a-4b
(P-Q)(P+Q)=P^2-Q^2