Question

7. Is (s + t)^2 equivalent to s^2 + 2st + t^2? Explain or show your reasoning.

Answer 1

Yes, (s + t)^2 is equivalent to s^2 + 2st + t^2. This can be shown through the process of expanding the expression (s + t)^2 using the FOIL method (multiplying first, outer, inner, and last terms).

First, we can rewrite (s + t)^2 as (s + t)(s + t).

• The first terms are s and s
• The outer terms are s and t
• The inner terms are t and s
• The last terms are t and t

Now, we do the multiplication and combine like terms:

s*s + s*t + t*s + t*t

s^2 + st + st + t^2

s^2 + 2st + t^2