Verified answer

(√3 - √5)( √3 - √5)

------------------------------------

Remember to use the FOIL rule : Front, outside, inside, last

(√3)(√3) - (√3)(√5) - (√5)(√3) + (√5)(√5)

√9 - √15 - √15 + √25

3 - √15 - √15 + 5

8 - √15 - √15

8 - 2√15

(√3 - √5)( √3 - √5) = (√3)² - 2(√3)(√5) + (√5)² = 3 - 2√15 + 5 = 8-2√15

So you have 8 - 2√15 which can be factored into 2(4-√15)

Not different answers, different forms of the same answer. Algebraic expressions can often be presented in different but equivalent forms.

All the answers are the same, no different answers:

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

(√3 - √5)( √3 - √5)

= √3^2 - 2√3√5 + √5^2

= 3 - 2√15 + 5

= 8 - 2√15

unless you mean (√3 - √5)( √3 + √5)

then it would be (a-b)(a+b) = a^2 - b^2

so (√3 - √5)( √3 + √5) = 3-5 = -2

(√3 - √5)(√3 - √5)

(√3)^2 - √15 - √15 + (√5)^2

3 - 2√15 + 5

8 - 2√15

or

2(4 - √15)

they are the same answer, it depends on how your teacher wants it presented.

2(4 - √15) is the factored form of 8 - 2√15

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

a=√3 and b=√5 so a^2=3, ab=√(15) and b^2=5

so you get 3-2√(15)+5=8-2√(15)

I hope this was among your answers. Note that you can check the answer with a calculator

3 - √15 - √15 + 5

8 - 2√15

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

(√3 - √5)( √3 - √5) = 3 - 2*sqrt(3)*sqrt(5) + 5

= 8 - 2*sqrt(3)*sqrt(5)

= 8 - 2*sqrt(15) <<<

expand + simplify

8-2 sqrt(15)

sqrt 3 - sq rt 5

sq rt 3-sq rt 5

======================

- sq rt 15 - sq rt 25

sqrt 9 -sq rt 15

--------------------------------------------------

sq rt 9-2 sq rt 15- sq rt 25

3-2 sq rt 15-5

-2-2 sqrt 15