In Calculus, but need help with an Algebra question!

What is ((2sqrt(1-x^2))/sqrt2)^2?

Exponents distribute over multiplication and division.

so this will become:
(2)^2 (√(1-x^2))^2 / (√2)^2

= 4 (1-x^2) / 2

= 2(1-x^2)

= 2-2x^2

Or you can factor it all out:
2(1-x^2) <--- (1-x^2) is a difference of squares...

2(1-x)(1+x)

...2√(1 - x^2)
[-------------------]^2
......√(2)

....4√(1 - x^2)^2
=-------------------------
.......√(4)

.....4(1 - x^2)
=--------------------
.........2

=2(1 - x^2)

=- 2(x^2 - 1)
= - 2(x + 1)(x - 1) answer//

[(2sqrt(1-x^2)) / sqrt2]^2 = [(sqrt(2)*sqrt(1-x^2)]^2 = 2(1-x^2) >========< ANSWER

2(1-x)(1+x)

(2√(1−x²)/√2)²

= 2² √(1−x²)² / √2²

= 4 (1−x²) / 2

= 2 (1−x²)

= 2 (1−x) (1+x)