Question

Evaluate each expression if $x=4,y=-2,$and $z=6$

$x+{\left(y-1\right)}^3$

Short answer

Expression$x+{\left(y-1\right)}^3$ results into $-23$.

Step-by-step solution

- Order of simplification

To evaluate any expression involving more than one operation, follow the below order of operations:

• First evaluate expressions inside grouping symbols like parentheses ( ) or brackets [ ].
• Evaluate the exponents.
• Perform Multiplication and division from left to right.
• Perform addition and subtraction from left to right.

- Substitute given values

Simplify parentheses by subtracting 1 from $y$.

Simplify power and then add resultant with $x$.

Substitute 4 for$x$ and$-2$ for$y$ into given expression

$x+{\left(y-1\right)}^3=4+{\left(-2-1\right)}^3$

- Simplify 4+-2-13

Follow order of simplification

$-2-1=-3$

Then

$\begin{array}{c}{\left(-2-1\right)}^3={\left(-3\right)}^3\\ =-27\end{array}$

Finally

$4+\left(-27\right)=-23$

Thus, $x+{\left(y-1\right)}^3=-23$