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Welcome to our Math lesson on Square of a Sum, this is the second lesson of our suite of math lessons covering the topic of Special Algebraic Identities Obtained through Expanding, you can find links to the other lessons within this tutorial and access additional Math learning resources below this lesson.
The square of a sum, otherwise known as the square of a binomial, is an algebraic expression of the type
where a and b are the terms of the binomial. The raise in power is equivalent to the multiplication of two equal terms, i.e.
we can find the expanded form of this expression by using the same procedure as in the expression
i.e. applying the FOIL method, where a = c and b = d. In this way, we obtain
Since a · a = a2; b · b = b2 and a · b = b · a, we obtain
The last expression represents the right part of the first special algebraic identity
which tells us how to expand the square of a sum.
Two friends decide to invest in cryptocurrency as they are convinced that after one year their capital will become the square of the original in value. The first friend who possesses the initial capital (A) proposes to join the capital (B) of the second friend and invest as a single entity. The second friend however, opposes this opinion and proposes to have the investments separated. Which of the two friends is right in his reasoning?
If the capitals are invested as a single entity (as the first friend suggested), the final capital by the end of the year will be
If capitals are invested separately (as the second friend suggested), the total capital by the end of the year will be
It is clear that
because the first amount has a non-zero 2AB term (both initial capitals are assumed as greater than zero; otherwise it is meaningless to speak about investment).
Therefore, the proposal of the first friend is more favourable, so his reasoning is right.
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