Skill: Evaluate algebraic expressions by substitution

To evaluate an algebraic expression by substitution:

1. Replace each variable with its assigned value.
2. Put negative numbers in parentheses.
3. Evaluate using the correct order of operations:
   • grouping symbols,
   • exponents,
   • multiplication or division,
   • addition or subtraction.

Example: Evaluate

$$2a^2-3b+5$$

when $a=-2$ and $b=-1$.

Step 1: Substitute the values.

Replace $a$ with $-2$ and $b$ with $-1$:

$$2(-2)^2-3(-1)+5$$

The parentheses around the negative numbers help show exactly what is being substituted.

Step 2: Evaluate the exponent.

$$(-2)^2=4$$

So the expression becomes

$$2(4)-3(-1)+5$$

Step 3: Multiply.

$$8+3+5$$

Notice that $-3(-1)=+3$.

Step 4: Add.

$$8+3+5=16$$

Therefore,

$$\boxed{16}$$