State whether the following equations are sometimes, always or never true.

Question

a) a^2-2ab-b^2= (a-b)^2, bis not equal to 0

b) a^2+ b^2= (a+b)(a+b)

c) a^2-b^2= a^2-2ab+b^2

d) (a=b)^2 = a^2+2ab+b^2

I don't understand what these questions are exactly asking. Could someone please explain?

Answer 1

it is asking if the left is the same as the right
look at a
(a-b)(a-b) = a^2 -2ab + b^2 Always
then b
(a+b)(a+b) = a^2 + 2ab + b^2 NOT a^2+b^2
and is ONLY true if a or b is zero
same problem with c
You have a typo in d but if that is a + sign then true (a+b)(a+b)=a^2+2ab+b^2

Answer 2

Thank you