EVALUATE ALGEBRAIC EXPRESSIONS
When you are asked to evaluate algebraic expressions, you will follow these steps:
1) substitute the given values for the variables
2) simplify the expression following the order of operations.
EXAMPLES:
For #'s 1-3, evaluate the following algebraic expressions for the given values.
Let x = 2 y = -1 z = 3 a = 0 b = -5.
1) 2xy + ab - yzb given expression
2(2)(-1) + 0(-5) - (-1)(3)(-5) substitute given values
-4 + 0 - 15 simplify multiplication
-19 add/subtract
2) 3 - b(2x + 5b) given expression
3 - (-5)[2(2) + 5(-5)] substitute given values
(note: you can use different grouping symbols to emphasize the operations)
3 + 5[4 - 25] simplify multiplication within brackets
3 + 5[-21] +/- within brackets
3 + -105 multiply
-102 add/subtract
3) 4xy5 - 2ab + (z + y)3 given expression
4(2)(-1)5 - 2(0)(-5) + (3 + -1)3 substitute given values
4(2)(-1)5 - 2(0)(-5) + (2)3 simplify within parenthesis
4(2)(-1) - 2(0)(-5) + 8 simplify powers/exponents
-8 + 0 + 8 simplify multiplication
0 add/subtract
4) 9/5C + 32 = F is the formula to convert degrees in Celsius (C) to degrees in Fahrenheit (F).
(The U.S. uses Fahrenheit while the rest of the world uses Celsius. Therefore, this formula is a wise one to know if you plan on traveling and want to know what the day's temperature is.)
The local news in Barcelona, Spain, announces it is 35 degrees Celsius. How will you dress?
F = 9/5(35) + 32 substitute given value into the formula
F = 63 + 32 simplify multiplication
F = 95 degrees add/subtract
Now that you did this quick computation, you know to dress in shorts and a top.
5) The formula for interest earned is I = p - p(1 + rt) where I is the interest, p is the principal, r is the interest rate and t is the time.
How much interest will you earn if you invest $2000 at 2% interest rate for 3 years?
I = 2000 - 2000(1 + 0.02(3)) substitute given values (% needs to convert to decimal)
I = 2000 - 2000(1 + 0.06)
I = 2000 - 2000(1.06)
I = 2000 - 2120
I = $120
6) The formula for work of an object is W = 0.5m(V2)2 - 0.5m(V1)2 where m is mass, V2 is the second velocity and V1 is the first velocity.
How much work is done if m = 40, V2 = 30 and V1 = 20?
W = 0.5(40)(30)2 - 0.5(40)(20)2 substitute given values
W = 0.5(40)(900) - 0.5(40)(400)
W = 18000 - 8000
W = 10,000