Find the value of n such that each expression is a perfect square trinomial. p^2+10p+n

 
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The first two terms in the trinomial need to commence a perfect square. A perfect square of a number that is expressed as x+a is x^2+2ax+a^2. In the question 2a would correspond to 10, therefore a=5 and n=25. Every value of p will now give a trinomial which is (p+5)^2.

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