Question

In the following exercises, evaluate each expression.

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

Short answer

The value is 42.

Step-by-step solution

Step 1. Given Information:  

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

Step 2. Substitute the values:  

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

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

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.

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

Step 4. Multiply:  

Perform multiplication from left to right.

$36-6+12$

Step 5. Perform Subtraction: 

Subtract 6 from 36 in the obtained expression.

$30+12$

Step 6. Perform Addition: 

Add 30 and 12 in the obtained expression.

$30+12=42$

Step 7. Conclusion: 

The value obtained is 42.