Questions: Evaluate the expression for the given values of the variables. ((3 x-z)^2+9 y) where (x=6, y=3), and (z=2)

Transcript text: Evaluate the expression for the given values of the variables. $(3 x-z)^{2}+9 y$ where $x=6, y=3$, and $z=2$ $\square$ Question Help: $\square$ Video Message instructor Calculator Submit Question

Solution

Solution Steps

To evaluate the expression $(3x - z)^2 + 9y$ for the given values of the variables $x = 6$, $y = 3$, and $z = 2$, we will substitute the values of $x$, $y$, and $z$ into the expression and then compute the result.

Step 1: Substitute the Given Values into the Expression

Given the expression $(3x - z)^2 + 9y$ and the values $x = 6$, $y = 3$, and $z = 2$, we substitute these values into the expression: \[ (3 \cdot 6 - 2)^2 + 9 \cdot 3 \]

Step 2: Simplify Inside the Parentheses

First, simplify the expression inside the parentheses: \[ 3 \cdot 6 - 2 = 18 - 2 = 16 \]

Step 3: Square the Result

Next, square the result obtained from the previous step: \[ 16^2 = 256 \]

Step 4: Multiply and Add

Now, multiply $9$ by $3$ and add it to the squared result: \[ 256 + 9 \cdot 3 = 256 + 27 = 283 \]