factor each polynomial
m4-81
isn't this the difference of two squares? And after you factor it that way, you might have another term that is the difference of two squares.
To factor the polynomial m^4 - 81, we can use the difference of squares formula. The formula states that when you subtract two perfect squares, such as a^2 - b^2, the result can be factored as (a + b)(a - b).
In our given polynomial, m^4 - 81, we can rewrite 81 as 9^2, which is a perfect square. So now we have m^4 - 9^2, which is in the form of a^2 - b^2.
Using the difference of squares formula, we can factor the given polynomial as (m^2 + 9)(m^2 - 9).
Now we further simplify the factorization. The second factor, m^2 - 9, is also a difference of squares. 9 can be written as 3^2, so m^2 - 9 can now be factored as (m + 3)(m - 3).
Therefore, the final factored form of the polynomial m^4 - 81 is (m^2 + 9)(m + 3)(m - 3).