Question

factor m^4-1

Answer 1

@KimB do you know the expansion of \(a^2-b^2\)??

Answer 2

Try to look at this problem as a difference of squares, with the square root of m^4 being m^2. Thus, you can factor it as: (m^2 +1)(m^2 -1).
But, (m^2-1) is also a perfect square, so you can factor that as (m+1)(m-1).

Write all three terms to get your final factorization: (m^2+1)(m+1)(m-1).

Answer 3

I am going to provide a little example.\[16x^4 - 81\implies(2x)^4 -(3)^4\implies((2x)^2)^2 - (3^2)^2 \]Now, what @ash2326 provided comes in.

Answer 4

\[((2x)^2 - 3^2)((2x)^2 + 3^2) \implies (2x + 3)(2x - 3)(4x^2 + 9) \]