If you have a^ + b^= (a+b)(a+b).

Is this always true, never true, or sometimes true?

Explain.

if i understand what you are saying:

FOIL:
(a+b)(a+b)

a^2+ab+ab+b^2=

a^2+2ab+b^2

so never true!!

To determine if the equation a^ + b^ = (a + b)(a + b) is always true, never true, or sometimes true, let's consider different scenarios.

First, let's expand (a + b)(a + b):
(a + b)(a + b) = a(a + b) + b(a + b)
= a^ + ab + ab + b^
= a^ + 2ab + b^

Now, let's compare this expression to the given equation. We have:
a^ + b^

Clearly, a^ + b^ and a^ + 2ab + b^ are not the same.

Therefore, the equation a^ + b^ = (a + b)(a + b) is sometimes true, but not always true. It depends on the values of a and b.