>> Welcome to a lesson on evaluating Algebraic expressions.
An expression in which some or all of the terms contain variables is an algebraic expression
or a variable expression.
If the value of the variables is known we can evaluate the expression,
so to evaluate an algebraic or variable expression we substitute the value
of the variables into the expression and then evaluate using the order of operations.
So for example if we have the expression 5 x minus 12 and we're also given
that x equals 17 we replace the variable x with the value of 17
and then the evaluate the expression, so here we'd have 5 times 17 minus 12,
well 5 times 17 is 85, then 85 minus 12 is equal to 73.
Let's go ahead and review the order of operations before we do a few more examples.
So remember there are four steps to the order of operations,
number 1 we will evaluate inside the parentheses or grouping.
Number 2 we'll evaluate the exponents.
Number 3 we will multiply and divide from left to right as it occurs
and number 4 we will add and subtract from left to right.
So let's go ahead and look at several examples.
So here we're given that x equals negative 3, y equals 7 and z equals negative 2
and we want to evaluate x minus 3 y plus 7.
So we'll replace x with negative 3 and y with positive 7,
so I have negative 3 minus 3 times 7 plus 7.
Now following the order of operations we're going to multiply next
so minus 3 times 7 becomes minus 21, now we work our way from left to right.
Subtracting and adding so we will have negative 3 minus 21 that's negative 24,
negative 24 plus 7 gives us negative 17.
This next example is the same process, we have 2 times x squared
but x is now negative 3 plus 5 times y,
y is 7 minus z to the third power and z is equal to negative 2.
So now we'll evaluate this using the order of operations.
There's nothing we can do inside the parentheses so next we'll take a look at the exponents,
negative 3 squared would be positive 9 and negative 2 raised
to the third power would be equal to negative 8.
Now we'll go ahead and multiply, so 2 times 9 is equal to 18 plus 5 times 7 is equal to 35
and here we have minus negative 8 and that will become plus positive 8.
Now performing the addition from left to right we have 18 plus 35 plus 8,
18 plus 35 would be 53, plus 8 would be 61.
Now we have y equals positive 2 and we want to evaluate this expression here so we replace y
with positive 2 next there's no parentheses that we can simplify, there's no exponent
so we will multiply and divide now from left to right.
Here we have a fraction, this does mean 9 divided by 2 so it really depends on if we want
to have our final answer in fraction form or decimal form, let's go ahead and rewrite this
in decimal form so 9 divided by 2 would be 4.5, minus 8 times 2 that's 16 plus 2.
Now we'll perform the addition and subtraction from left to right
so we have 4.5 minus 16 it's going to be negative 11.5 plus 2 which equals negative 9.5,
if we wanted this in fraction form that would be the same as negative 9 1/2
or we could write this as negative 19 halves,
all of which are equivalent just in different forms.
Here we have x equals 3 and y equals negative 5 so we will have 4 times x
which is 3 minus 3 times y squared but y is negative 5 so I have negative 5 squared.
Next we will evaluate negative 5 squared,
that will be 4 times 3 minus 3 times negative 5 squared is positive 25, now we'll multiply
so 3 times 4 would be 12 minus 3 times 25 is equal to 75
and then finally 12 minus 75 is equal to negative 63.
Let's try another, here we have x equals negative 2 so we'll substitute negative 2
in for x so we will have 3 times negative 2
to the third power minus negative 2 squared plus 2 times negative 2 plus 9.
Next we will simplify the exponents, negative 2 raised to the 3rd power is equal negative 8.
Negative 2 squared would be positive 4
and now we'll multiply 3 times negative 8 equals negative 24,
here we'll have minus 4 plus 2 times negative 2 that's negative 4 and then plus 9.
So now we'll add and subtract from left to right so negative 24 minus 4 that will be negative 28
and negative 28 plus negative 4 that will be negative 32
and then lastly negative 32 plus 9 equals negative 23.
Let's go and take a look at one more example.
Here we have x equals 2 and y equals negative 3
so the numerator will be 2 squared times negative 3 squared over x squared
which would be 2 squared minus 2 times y to the third will become negative 3 to the third.
So what we'll do here is evaluate the numerator and the denominator separately
and then lastly simplify the fraction.
So 2 squared would be 4 and negative 3 square would be 9, for the denominator we're going
to have 4 minus 2 times negative 3 cubed is equal to negative 27.
Our numerator is going to be 36 and the dominator will have 4 minus negative 54
which will become plus 54, so this fraction is 36 over 58, these both have a common factor of 2
so in simplified form the fraction would be 18 over 29.
I hope you found this video helpful and thank you for watching.
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