Carcass wrote:
Both x and y are integers. Which of the following expressions must be the square of an integer?
Indicate all such expressions.
A. \((x+y)(x-y)+8xy+17y^2\)
B. \(9x^4-12x^2y^2+4y^4\)
C. \(x^6+2x^3y^3+y^6\)
A. Given: \((x+y)(x-y)+8xy+17y^2\)
Expand and simplify the first product: \(x^2-y^2+8xy+17y^2\)
Simplify: \(x^2+8xy+16y^2\)
Factor: \((x + 4y)(x + 4y) = (x + 4y)^2\)
WORKS!
B. Given: \(9x^4-12x^2y^2+4y^4\)
Factor to get: \((3x^2-2y^2)(3x^2-2y^2) = (3x^2-2y^2)^2\)
WORKS!
C. Given: \(x^6+2x^3y^3+y^6\)
Factor to get: \((x^3+y^3)(x^3+y^3) = (x^3+y^3)^2\)[/quote]
WORKS!
Answer: A, B, C
Cheers,
Brent