Question

Evaluate$3a^2-2ab+c$ for the values given.

$a=-1,b=0,c=11$

Short answer

The value of the expression is 14.

Step-by-step solution

Step 1. State the concept used.

• To get rid of a number in addition from one side, subtract the same number from both sides of the equal sign.
• To get rid of a number in subtraction from one side, add the same number on both sides of the equal sign.
• To get rid of a number in multiplication from one side, divide the same number from both sides of the equal sign.
• To get rid of a number in the division from one side, multiply the same number on both sides of the equal sign.

Rules of Addition/ Subtraction:

• Two numbers with similar signs always get added and the resulting number will carry the similar sign.
• Two numbers with opposite signs always get subtracted and the resulting number will carry the sign of the larger number.

Rules of Multiplication/ Division:

• The product/quotient of two similarsign numbers is always positive.
• The product/quotient of two numbers with opposite signs is always negative.

Step 2. Substitute the values. 

In order to calculate $3a^2-2ab+c$, substitute $-1$ for $a,0$ for $b$, and 11 for $c$.

$3a^2-2ab+c=3{\left(-1\right)}^2-2\left(-1\right)\left(0\right)+11$

Step 3. Simplify the expression.

Further, simplify the expression by applying the rules of BODMAS.

$3a^2-2ab+c=3{\left(-1\right)}^2-2\left(-1\right)\left(0\right)+11$

$$\begin{gathered} =3+0+11 \\ =14 \end{gathered}$$

Thus, the value of the expression is 14.