Evaluate Algebraic Expressions

Evaluate Algebraic Expressions

To evaluate an algebraic expression means to —
• replace the variable(s) in the expression with the number value(s) given,
• place the given values in parentheses,
• simplify the expression using the order of operations, and
• determine the end result.

Example 1

Evaluate  4(x2 + 5x) − 2y, given that x = 2 and y = -3.

Substitute 2 for x and -3 for y in the given expression:
4[(2)2 + 5 · (2)] − [2( -3)]

Simplify using the order of operations:
4[4 + 10] − [-6]
4 [14] − [-6]
56 + 6
62

Example 2
Kinetic energy is given by the formula K = mv2.  Find the amount of energy when m = 10 kg and v = 6 m/s(The unit of energy is the Joule.)

Substitute 10 for m and 6 for v in the given formula:
× (10) × (6)2

Simplify using the order of operations:
× 10 × 36
5 × 36
180 J

Practice

Substitute the given values for the variables to evaluate each expression.

1)  Evaluate  3(x2 + 4x) − 3y when x = -5 and y = 3

2)  Evaluate x2y  for x = -3 and y = -4

3)  Evaluate  (b − d)2  when b = 9 and d = -3

4)  Evaluate m4 + 2m3 − m2 + 8 for m = -2

5)  Evaluate y =  3x + 1 for x = -5

6)  In baseball, a pitcher's earned run average (ERA) is computed with the expression , where r is the number of earned runs allowed and p is the number of innings pitched.  If a pitcher has allowed 5 earned runs over 12 innings pitched, what is his ERA?