Question

factor
$m^4 - 1$
hint: difference of two squares
$\bigcirc (m^3 - 1)(m + 1)$
$\bigcirc (m - 1)^2(m + 1)^2$
$\bigcirc m^3(m - 1)$
$\bigcirc (m^2 + 1)(m - 1)(m + 1)$

Explanation:

Step1: Apply difference of squares

The expression \( m^4 - 1 \) can be written as \( (m^2)^2 - 1^2 \). Using the difference of squares formula \( a^2 - b^2=(a + b)(a - b) \), we get:
\( (m^2 + 1)(m^2 - 1) \)

Step2: Factor \( m^2 - 1 \)

The term \( m^2 - 1 \) is also a difference of squares (\( m^2 - 1^2 \)). Applying the difference of squares formula again:
\( (m + 1)(m - 1) \)

Step3: Combine the factors

Substitute the factored form of \( m^2 - 1 \) back into the expression from Step 1:
\( (m^2 + 1)(m + 1)(m - 1) \)

Answer:

\( (m^2 + 1)(m - 1)(m + 1) \) (corresponding to the option \((m^2+1)(m - 1)(m + 1)\))