Question

Evaluate each expression if$w=6,x=0.4,y=\frac{1}{2},$ and$z=-3$

48.${\left(x-y\right)}^2-2wz$

Short answer

Expression ${\left(x-y\right)}^2-2wz$ results into $36.01$

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

Substitute $\frac{1}{2}$for $y$, $-3$for z, 6 for $w$and $0.4$ for $x$into given expression

${\left(x-y\right)}^2-2wz={\left(0.4-\frac{1}{2}\right)}^2-2\times 6\times \left(-3\right)$

- Simplify 0.4-122-2×6×-3

• To evaluate the value of the given expression, first simplify the expression inside the parenthesis and then expand the exponent.
• Multiply 2 with w and then with z
• Finally subtract resulting terms from left to right
  $\begin{array}{c}{\left(0.4-\frac{1}{2}\right)}^2-2\times 6\times \left(-3\right)={\left(-0.1\right)}^2-12\left(-3\right)\\ =0.01+36\\ =36.01\end{array}$
  Thus, value of ${\left(x-y\right)}^2-2wz$is$36.01$