Question

In the following exercises, evaluate each expression.

$3x^2-4xy+2y^2$when$x=-2$and$y=-3$

Short answer

The value is 6.

Step-by-step solution

Step 1. Given Information:

The given expression is $3x^2-4xy+2y^2$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 $3x^2-4xy+2y^2$.

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

Step 3. Calculate the exponents: 

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

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

Step 4. Multiply:   

Perform multiplication from left to right.

$\begin{array}{rcl}3·4-4\left(-2\right)\left(-3\right)+2·9& =& 12-4·6+18\\ & =& 12-24+18\end{array}$

Step 5. Perform Subtraction:  

Subtract 24 from 12 in the obtained expression.

$-12+18$

Step 6. Perform Addition:  

Add 18 and $-12$in the obtained expression.

$-12+18=6$

Step 7. Conclusion:  

The value obtained is 6.