Q2. - Algebra 1

Question

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

 $a=-3,b=-2,c=3$

Step-by-Step Solution

Answer

The value of the expression is 18.

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 similar sign 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 $-3$ for $a, -2$ for $b$, and 3 for $c$.

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

Step 3. Simplify the expression.

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

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

                       $$\begin{gathered} =3\times 9-2\times 6+3 \\ =27-12+3 \\ =15+3 \\ =18 \end{gathered}$$