Question

Evaluate:$4x^2-xy+5y^2$when$x=-2,y=3$.

Short answer

The value is 67.

Step-by-step solution

Step 1. Given Information. 

The given expression is $4x^2-xy+5y^2$and the values of the variables are $x=-2$and $y=3$.

Step 2. Substitute the values.

Substitute $-2$for $x$and 3 for $y$into the given expression $4x^2-xy+5y^2$.

$4{\left(-2\right)}^2-\left(-2\right)\left(3\right)+5{\left(3\right)}^2$

Step 3. Calculate the exponents.

The value of the exponents are ${\left(-2\right)}^2=4$and ${\left(3\right)}^2=9$. Simplify the exponents in the obtained expression.

$4·\left(4\right)-\left(-2\right)\left(3\right)+5·\left(9\right)$

Step 4. Multiply. 

Perform multiplication from left to right.

$16-\left(-6\right)+45$

Step 5. Simplify.

Add and subtract from left to right.

$\begin{array}{rcl}16+6+45& =& 22+45\\ & =& 67\\ & & \end{array}$

Step 6. Conclusion.

The required value is 67.