Hi Confused.
With the first expression
81x3-3000
We see that we are dealing with some very large numbers. As Tkhunny said, we must find the GCF of
81 and
3000 by asking what factors they share. As it turns, they share a common factor of
3.
[MATH]81\div 3 = 27[/MATH] and [MATH]3000\div 3 = 1000[/MATH] . This means we can factor out
3 from both terms. Thus we will write
3(27x3-1000)
Next comes the Difference of Cubes that Tkhunny described. What we must first do is ensure we clearly understand which term is
a in our expression and which is
b, because subtraction is non commutative and the order here does matter. In other words, if you plug in our
"a" which is
27 into the
"b" in our formula, we will receive the wrong answer. The formula for the difference of cubes is
We know
a=27
b=1000
Plugging in our known values into the formula will produce the answer we need. Sometimes we may need to further factor of the value(s) inside the parenthesis, but it will not be necesary here as it cannot be factored further.