## Proof Exercise #2 Continuation 3

Yes.

We will replace (p - q)^2 in the inequality by its expansion.

Its expansion is p^2 - 2pq + q^2.

Therefore, we now have the inequality, "0 is less than or equal to the quantity (p^2 - 2pq + q^2).

What, from the following list, do you think, is what we'll do next?

choice #1: Replace p by q, and q by p.

choice #2: Replace p^2 by x, and replace q^2 by y.

choice #3: Replace p^2 by p^3, and replace q^2 by q^3.

choice #4: Replace p^2 by (p + 1)^, and replace q^2 by (q + 1)^2.

choice #5: Replace 0 in the inequality by (p + q)^2.

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We will replace (p - q)^2 in the inequality by its expansion.

Its expansion is p^2 - 2pq + q^2.

Therefore, we now have the inequality, "0 is less than or equal to the quantity (p^2 - 2pq + q^2).

What, from the following list, do you think, is what we'll do next?

choice #1: Replace p by q, and q by p.

choice #2: Replace p^2 by x, and replace q^2 by y.

choice #3: Replace p^2 by p^3, and replace q^2 by q^3.

choice #4: Replace p^2 by (p + 1)^, and replace q^2 by (q + 1)^2.

choice #5: Replace 0 in the inequality by (p + q)^2.

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