Determine whether each binomial is the difference of two square. If so, factor it. If not, explain why.
-m^6
To determine whether a binomial is the difference of two squares, we need to check if it can be written as the square of one term minus the square of another term.
In this case, the binomial is -m^6. To check if it is the difference of two squares, we need to look for a perfect square term.
First, let's rewrite -m^6 as (-m^3)^2. By doing this, we can see that -m^6 can indeed be written as the square of one term, -m^3, subtracted from the square of another term, 0.
So, -m^6 is the difference of two squares. To factor it, we can use the formula:
a^2 - b^2 = (a + b)(a - b)
Applying this formula, we can factor -m^6 as the difference of squares:
(-m^3)^2 - 0^2 = (-m^3 + 0)(-m^3 - 0)
= (-m^3)(-m^3)
= m^3*(-m^3)
= -m^6
Therefore, the factored form of -m^6 is -m^3 * -m^3.