Question

For what values of x and y is the equation (x2 + y2)2 = (x2 – y2)2 + (2xy)2 true?

A) all values of x, and all values of y
B) all values of x, but only positive values of y
C) only positive values of x, but all values of y
D) only positive values of x, and only positive values of y

Factor: 27a3 + 64b3
A) (3a + 4b)(9a2 + 12ab + 16b2)
B) (3a + 4b)(9a2 - 12ab + 16b2)
C) (3a - 4b)(9a2 + 12ab + 16b2)
D) (3a - 4b)(9a2 + 12ab - 16b2)

if you could please explain thank you.

Answer 1

A) all values of x, and all values of y

B) (3a + 4b) (9a² − 12ab + 16b²)

Explanation:

(x² + y²)² = (x² − y²)² + (2xy)²

x⁴ + 2x²y² + y⁴ = x⁴ − 2x²y² + y⁴ + 4x²y²

x⁴ + 2x²y² + y⁴ = x⁴ + 2x²y² + y⁴

27a³ + 64b³

(3a)³ + (4b)³

(3a + 4b) (9a² − 12ab + 16b²)