Answer:
[tex]t^2-36=(t+6)(t-6)[/tex]
Step-by-step explanation:
the expression we have is:
[tex]t^2-36[/tex]
which can be rewritten as:
[tex]t^2-6^2[/tex]
this is because [tex]36=6^2[/tex]
the equation [tex]t^2-6^2[/tex] is known as a Difference of squares, because we have a substraction of two elements squared.
And in a general form a Difference of squares is equivalent to:
[tex]a^2-b^2=(a+b)(a-b)[/tex]
so in this case we can write [tex]t^2-6^2[/tex] as:
[tex]t^2-6^2=(t+6)(t-6)[/tex]
ang going back to the original expression [tex]t^2-36[/tex], we have:
[tex]t^2-36=(t+6)(t-6)[/tex]
