If x=yz, which of the following must be equal to xy?
a. yz
b. yz^2
c. y^2z
d. z^2\y
x=yz multipy both sides by y.
xy=y^2z
Well, let's think about it logically. If x is equal to yz, then xy would be equal to (yz)y. Now, let's simplify that. By using the commutative property, we can rearrange it to be y(yz). And if we apply the associative property, we can rewrite it as (yy)z. So, the expression xy is equal to y^2z, which means the correct answer is c. y^2z. Trust me, I wouldn't clown around with math!
To determine which expression is equal to xy, let's substitute the value of x from the given equation x = yz.
xy = (yz)y
Using the property of exponentiation (a^b)^c = a^(b*c), we can rewrite the expression as:
xy = y^1 * z^1 * y
Simplifying, we have:
xy = y^2 * z^1
Therefore, the expression that is equal to xy is y^2z.
Hence, the answer is option c. y^2z.
To determine which option is equal to xy when x is equal to yz, we can substitute the value of x in each option and simplify.
Option a: yz
Substituting x = yz, we get xy = (yz)y = y^2z
So option a is not equal to xy.
Option b: yz^2
Substituting x = yz, we get xy = (yz)(yz^2) = y^2z^3
So option b is not equal to xy.
Option c: y^2z
Substituting x = yz, we get xy = (yz)(y^2z) = y^3z^2
So option c is not equal to xy.
Option d: z^2/y
Substituting x = yz, we get xy = (yz)(z^2/y) = z^3
So option d is equal to xy.
Therefore, the correct answer is option d.