SOLUTION: i have the answer to (p+6)^2 as: p^2 +12p +36 i can see how the p^2 and the +36 are done but i can not figure out how to arrive at the +12p. your help will be greatly appreciate

(p + 6)²

When something is squared it is multiplied by itself.
So write it as

(p + 6)(p + 6)

Then use the "FOIL" method to multiply it out

F = FIRSTS = p·p = p²
O = OUTERS = p·6 = 6p
I = INNERS = 6·p = 6p
L = LASTS = 6·6 = 36

So write the sum of those four terms

p² + 6p + 6p + 36

The two terms in the middle are like terms,
So 6p + 6p = 12p

and the final answer is

p² + 12p + 36

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You can always write the binomial down twice and use FOIL
as above, or you can learn the shortcut rule for squaring
a binomial:

 

Edwin