Q48. - Algebra 2

Question

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

48. ${\left(x-y\right)}^2-2wz$

Step-by-Step Solution

Answer

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

Step 1 - 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.

Step 2 - Substitute given values

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

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

Step 3 - Simplify 0 . 4 - 1 2 2 - 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 $36.01$