Step-by-step explanation:
According to the form of difference of squares,
[tex] {x}^{2} - {y}^{2} = (x + y)(x - y)[/tex]
In the example, we need to factor m² - 49. This is factorable by difference of squares because m² and 49 are perfect squares.
So, we let the x² part be m² and the y² part be 49.
By setting x² = m² and y² = 49, we can see that x = m and y = 7 (take only the principal root).
And so, we have factored m² - 49,
[tex] {m}^{2} - 49 = (m + 7)(m - 7)[/tex]
which is (m + 7)(m - 7).
