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.