Determine the value of the absolute
value of 22 squared times 25 minus four times 22 squared all over negative seven
times 22 squared by identifying the greatest common factor.
We have this expression that has an
absolute value. And we want to determine exactly
what value this expression represents. However, our instructions have said
to find this value by identifying the greatest common factor. By identifying the greatest common
factor, we can first simplify our expression and secondly solve for the value.
A greatest common factor will be a
factor that is shared in the numerator and the denominator. Looking carefully here, we see that
we have 22 squared occurring twice in the numerator and once in the denominator. And this is where we need to be
very careful. Notice in the denominator we are
only doing multiplication. However, in the numerator, we have
some subtraction. 22 squared times 25 is a term
together, and four times 22 squared is another term. And that means we’ll need to do
some rearranging in the numerator.
Since both terms in the numerator
have a factor of 22 squared, we can undistribute that 22 squared and rewrite the
numerator as 22 squared times 25 minus four. This is because both 25 and four
were being multiplied by 22 squared. Once we do this, we can bring down
everything else from our expression. Our denominator is negative seven
times 22 squared. If we wanted to rearrange this
multiplication, we could write that as 22 squared times negative seven.
And at this point, we see that we
have a common factor in the numerator and the denominator. And that is the factor of 22
squared. 22 squared over 22 squared equals
one, which means we can simplify our expression to be the absolute value of 25 minus
four over negative seven. 25 minus four is 21. Then we have the absolute value of
21 over negative seven.
At this point, we’re ready to start
solving. 21 divided by negative seven is
negative three. And the absolute value of negative
three is positive three. And that means the value of our
initial expression is three.