Question

PLEASE ANSWER ASAP

expand and simplify the following:
a) (√6+√3)(√6-√3)
b)(√5-√2)(√2+√5)

Answer 1

I've attached the Answer

Explanation:

here it is

Answer 2

`(√(6)+√(3))(√(6)-√(3))=3`

`(√(5)-√(2))(√(2)+√(5))=3`

Explanation:

We want to simplify the expression:

`(√(6)+√(3))(√(6)-√(3))`

Notice that this is the difference of two squares pattern. Namely:

`a^2-b^2=(a+b)(a-b)`

If we let a = √6 and b =√3, we acquire:

`(a+b)(a-b)`

Expand accordingly:

`=a^2-b^2`

Back-substitute:

`=(√(6))^2-(√(3))^2`

Simplify:

`=6-3=3`

For the second expression, we have a similar pattern:

`(√(5)-√(2))(√(2)+√(5))`

We can first rewrite the expression (commutative property):

`=(√(5)-√(2))(√(5)+√(2))`

And if we let a = √5 and b = √2:

`=(a-b)(a+b)`

Expand accordingly:

`=a^2-b^2`

Back-substitute and simplify:

`=(√(5))^2-(√(2))^2=5-2=3`