Question

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

$a=5,b=-3,c=-9$

Short answer

The value of the expression is96.

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 5 for $a,-3$for $b$, and $-9$for $c$.

$3a^2-2ab+c=3{\left(5\right)}^2-2\left(5\right)\left(-3\right)+\left(-9\right)$

Step 3. Simplify the expression.

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

$3a^2-2ab+c=3{\left(5\right)}^2-2\left(5\right)\left(-3\right)+\left(-9\right)$

$$\begin{gathered} =3\times 25+30-9 \\ =75+21 \\ =96 \end{gathered}$$

Thus, the value of the expression is 96.