Question

find the expression that represents the length of the hypotenuse of a right triangle whose legs measure $2x^{2}-y^{2}$ and $2xy$.
a. $sqrt{4x^{4}+y^{4}}$
b. $2x^{2}+y^{2}$
c. $4x^{4}+y^{4}$
d. $sqrt{4x^{4}+8xy + y^{4}}$
please select the best answer from the choices provided
a
b
c
d

Explanation:

Step1: Apply Pythagorean theorem

Let $a=2x^2-y^2$, $b=2xy$, hypotenuse $c=\sqrt{a^2+b^2}$

Step2: Expand $a^2$

$$(2x^2-y^2)^2=4x^4-4x^2y^2+y^4$$

Step3: Expand $b^2$

$$(2xy)^2=4x^2y^2$$

Step4: Sum $a^2$ and $b^2$

$$4x^4-4x^2y^2+y^4+4x^2y^2=4x^4+y^4$$

Step5: Take square root

$$c=\sqrt{4x^4+y^4}$$

Answer:

A. $\sqrt{4x^{4}+y^{4}}$