The question asks about "these expressions" suggesting that a list of expression is given. In such circumstances would it be too much to expect that you make sure that there is something that is following?
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8p3 + 1 = (2p + 1)(4p2 - 2p + 1)
An equation if both expressions are equal
That means that the two expressions represent the same number.
equivalent
You can use them to find a variable. Lets say you have two equivalent expressions with the same variable... x + 2x - 42 = 0 2x - 28 = 0 If you combine these equivalent expressions you ahve... x + 2x - 42 = 2x - 28 In all of the expressions you have x = 7 There are also other applications but its confusing to explain.