Question

Find a pair of factors for each number by using the difference of two squares for the numbers 45,77,112

Answer 1

not sure what this means, but \(45=7^2-2^2\)

Answer 2

is this the kind of answer you are looking for?

Answer 3

since \(a^2-b^2=(a+b)(a-b)\) you can start with
\((a+b)(a-b)=77\) for example
since 77 factors as \(11\times 7\) that tells you
\[a+b=11\]
\[a-b=7\] and then you can solve for \(a\) and \(b\) by adding the two equations to get
\[2a=18\] and so \(a=9\) making \(b=2\) and thus
\[77=(9+2)(9-2)=9^2-2^2\]