4. If x = a + z and y = a - z, which of the following represents the product of x and y for every number a and z?
A. az
B. z^2
C. a^2
D. a^2 - z^2
E. a^2 - 2az - z^2
5. If x^3 (x to the third power) is equal to y^21z^12, and if x, y, and z are positive numbers, then x equals...
A. y^7z^4 over 3
B. y^7z^4
C. y^7z^12 over 3
D. y^7z^12
E. y^21z^12
A. az
B. z^2
C. a^2
D. a^2 - z^2
E. a^2 - 2az - z^2
5. If x^3 (x to the third power) is equal to y^21z^12, and if x, y, and z are positive numbers, then x equals...
A. y^7z^4 over 3
B. y^7z^4
C. y^7z^12 over 3
D. y^7z^12
E. y^21z^12
-
4. xy = (a + z)(a - z)
Multiply that out:
a*a + a*-z + z*a + z*-z
a^2 - az + az - z^2
a^2 - z^2; D
5. x^3 = y^21 * z^12
Cube root both sides (essentially, divide each exponent by 3):
x = y^7 * z^4; B
Multiply that out:
a*a + a*-z + z*a + z*-z
a^2 - az + az - z^2
a^2 - z^2; D
5. x^3 = y^21 * z^12
Cube root both sides (essentially, divide each exponent by 3):
x = y^7 * z^4; B