We want to evaluate the following expressions
for the given values and check on the graphing calculator.
So looking at our first expression here,
we want to evaluate this for x equals negative six
and y equals negative four.
So preform substitution, x squared will be
negative six squared minus y squared will
be negative four squared,
and because the bases are negative,
we do need these bases in parenthesis.
Negative six squared is equal to positive 36,
negative four squared is equal to positive 16,
giving us a difference of 20.
Lets go ahead and check this on the calculator.
Just to emphasize how important these parenthesis are,
if we did enter negative six squared,
without the parenthesis,
they should actually give us the opposite
of positive six squared or negative 36.
So when preforming substitution,
it is important to put parenthesis around the base.
Looking at our next expression, also copied below,
we want to substitute three for x and nine for y.
So we would have seven time the quantity three minus two
plus eight time the quantity nine squared
plus four.
And now following order of operations,
we want to simplify inside the parenthesis first,
here and here.
So we'd have seven times,
well, three minus two is just one,
and then we have plus eight
times,
nine squared is equal to 81.
So 81 plus four, inside the parenthesis,
So we have seven times one plus eight times 85.
And now we multiply.
Seven times one is seven.
Six times 85 is equal to 680,
and then finally we add 687 is the value of the expression,
given these values of x and y.
Checking on the calculator,
we'll enter this expression here.
So we have seven,
times the quantity
three minus two.
We can leave off the parenthesis here if we want.
So just three minus two,
close parenthesis,
plus eight,
times the quantity.
Again, because the base is positive nine,
we can leave the parenthesis off.
So we can just enter nine squared,
plus four,
close parenthesis
and enter.
Verifying our answer.
Looking at our next expression here,
we'll substitute six for x and negative three for y.
So, we'd have nine,
times six squared plus five
and then minus the quantity of y cubed
is going to be negative three cubed minus seven.
We simplify inside the parenthesis here and here
before subtracting.
So looking at our first set of parenthesis,
we begin by simplifying the exponents,
six squared is equal to 36.
So we'd have nine times 36 plus five.
Looking at the second set of parenthesis,
negative three cubes is equal to negative 27.
So we'd have negative 27 minus seven.
Still simplifying inside the parenthesis.
Here, we multiply nine times 36
is equal to 324.
So we have 324 plus five,
and then we have minus the quantity.
Here we'd have negative 27 minus seven, that's negative 34.
And then 324 plus five is equal to 329.
And then we have minus negative 34,
which becomes plus 34,
which equals 363.
Let's go ahead and check this.
To save some time I've already entered this,
lets just check it.
Looks good, press enter.
Which does verify our answer.
We want to evaluate the expression
for x equals negative two.
So lets substitute negative two for x.
So our numerator is going to be, negative two squared,
Plus three.
Your denominator is going to be,
negative two minus four and then we have plus five.
Remember when simplifying a fraction,
there are implied parenthesis
around the numerator and denominator.
So we'll simplify them separately,
and then simplify the fraction.
So looking at the numerator,
we simplify the exponents first.
Negative two squared is positive four.
So we have positive four plus three,
over here we have negative two minus four,
that's negative six,
plus five.
Which is equal to, this would be seven over negative six,
or just negative seven sixths,
plus five,
which divided, is five over one.
Now, to find this sum, we must obtain a common denominator,
which would be six.
So we multiply five over one by six over six.
So now we have a common denominator of six.
The numerator is negative seven,
plus 30,
which is equal to 23 sixths.
So this is equal to 23 sixths.
Lets go ahead and check this on the calculator.
We'll put the numerator in parenthesis,
we have open parenthesis, and then negative two squared,
plus three, close parenthesis, so there is the numerator.
Divided by,
in parenthesis,
for the denominator we have negative two minus four,
close parenthesis, so there is the denominator,
and then we have plus five.
Enter.
And math.
Enter. Enter.
Converts to a improper fraction,
which verifies our answer as correct.
I hope you found this helpful.