Question

find the product, simplify your answer
[(x+1)-5y][(x+1)+5y]

Answer 1

This is product of sum and difference of two expressions. First expression being (x+1) and the second being 5y.
That product can be presented as difference of squares of these two expressions like in:
\[x ^{2} - y ^{2} = (x+y)(x-y)\].
So your expression becomes

\[(x+1)^{2} - (5y)^{2} = x ^{2} +2x +1 - 25y^{2}\]