Write 3 different algebraic expressions that uses x,y, and z and simplifies to the given value when x=-3, y=-2, and z=-1. The expression should involve only multiplication or division. Values are: 1, -16, and 12.
x/y * y/x = 1
y*y*y*y*z = -16
x*y*y*z = 12
To find three different algebraic expressions using x, y, and z that simplify to the given values, we can use the given values and substitute them for x, y, and z in various expressions. Let's start by using multiplication and division.
Expression 1: \(\frac{{-16}}{{y}}\)
To find the value of this expression when x = -3, y = -2, and z = -1, substitute these values into the expression:
\(\frac{{-16}}{{-2}} = 8\)
Expression 2: \(x \cdot y \cdot z\)
Substituting the given values into the expression:
\((-3) \cdot (-2) \cdot (-1) = -6\)
Expression 3: \(\frac{{1}}{{y-z}}\)
Using the given values:
\(\frac{{1}}{{-2-(-1)}} = -\frac{{1}}{{3}}\) or approximately -0.333
So, the three different algebraic expressions that simplify to the given values when x = -3, y = -2, and z = -1 using only multiplication or division are:
Expression 1: \(\frac{{-16}}{{y}}\), which simplifies to 8
Expression 2: \(x \cdot y \cdot z\), which simplifies to -6
Expression 3: \(\frac{{1}}{{y-z}}\), which simplifies to -\(\frac{{1}}{{3}}\) (or approximately -0.333)