Question

Evaluate: $3x^2-2xy+6y^2$ when $x=1,y=-2$.

Short answer

The value is 31.

Step-by-step solution

Step 1. Given Information: 

The given expression is $3x^2-2xy+6y^2$and the values of the variables are $x=1$and $y=-2$.

Step 2. Substitute the values: 

Substitute 1 for $x$and $-2$for $y$into the given expression $3x^2-2xy+6y^2$.

$3{\left(1\right)}^2-2\left(1\right)\left(-2\right)+6{\left(-2\right)}^2$

Step 3. Calculate the exponents:

The value of the exponents are ${\left(1\right)}^2=1$and ${\left(-2\right)}^2=4$. Simplify the exponents in the obtained expression.

$3·1-2\left(1\right)\left(-2\right)+6·4$

Step 4. Multiply: 

Perform multiplication from left to right.

$3-\left(-4\right)+24$

Step 5. Perform Subtraction:

Subtract $-4$from 3 in the obtained expression.

$7+24$

Step 6. Perform Addition:

Add 7 and 24 in the obtained expression.

$7+24=31$

Step 7. Conclusion:

The required value is 31.